****** OPERATOR NEWS ***** No. 1 date: 1994.10.7 editied by Seung-Hyeok Kye (kye@math.snu.ac.kr) Dear Colleague, This is the first E-mail distribution of OPERATOR NEWS from Seoul National University. The main item of the NEWS will be announcement of the weekly seminar. 1994.10.14. Fri 10:00 Jang Sung Young (Ulsan Univ.) Crossed products of C*-algebras by semigroups of automorphisms, III 1994.10.28. Fri 10:00 Ko Eungil (Seoul N. Univ.) to be announced 1994.11.25. Fri 10:00 Lee Woo Young (Sung Kyun Kwan Univ.) Non-singularity and invertibility for a commuting pair 1994.11.25. Fri 16:00 Lee Woo Young (Sung Kyun Kwan Univ.) SNU Math Colloquium -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.2 date: 1994.10.19. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) The following is seminar schedule at Seoul National University 1994.10.28. Fri 10:00 Ko Eungil (Seoul N. Univ.) On the unilateral backward shift 1994.11.4. Fri 10:00 Kim Sung Geon (GARC) Norm or numerical radius attaining multilinear mappings and polynomials on Banach spaces 1994.11.25. Fri 10:00 Lee Woo Young (Sung Kyun Kwan Univ.) Non-singularity and invertibility for a commuting pair 1994.11.25. Fri 16:00 Lee Woo Young (Sung Kyun Kwan Univ.) SNU Math Colloquium -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.3 date: 1994.10.28. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) ** Seminar Schedule at Seoul National University ** 1994.11.4. Fri 10:00 Kim Sung Geon (GARC) Norm or numerical radius attaining multilinear mappings and polynomials on Banach spaces 1994.11.11. Fri 10:30 Cho Chong-Man (Hanyang Univ.) M-ideals of compact operators 1994.11.25. Fri 10:00 Lee Woo Young (Sung Kyun Kwan Univ.) Non-singularity and invertibility for a commuting pair 1994.11.25. Fri 16:00 Lee Woo Young (Sung Kyun Kwan Univ.) SNU Math Colloquium -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.4 date: 1994.11.11. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) Dr. Kenneth J. Dykema (Fields Institute, Waterloo) will be here, and give a series of lectures on "Free random variables and von Neumann algebras" from Feb. 13 (Mon) through Feb 18 (Sat), 1995, at 10:00 am everyday. More detailed information is available from Professor Sa-Ge Lee (02-880-6542). ** Seminar Schedule at Seoul National University ** 1994.11.18. Fri 10:00 Kim Hyoungsoon (Yonsei Univ.) Multipliers of C*-algebras 1994.11.25. Fri 10:00 Lee Woo Young (Sung Kyun Kwan Univ.) Non-singularity and invertibility for a commuting pair 1994.11.25. Fri 16:00 Lee Woo Young (Sung Kyun Kwan Univ.) SNU Math Colloquium -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.5 date: 1994.12.2. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) On Dec. 9 (Fri), MS candidates in Operator Algebras will present their theses from 10:00 am. This is the final meeting in this year. Dr. Kenneth J. Dykema (Fields Institute, Waterloo) will be here, and give a series of lectures on "Free random variables and von Neumann algebras" from Feb. 13 (Mon) through Feb 18 (Sat), 1995, at 10:00 am everyday. More detailed informations will be posted later, and available from Professor Sa-Ge Lee (02-880-6542). --------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.6 date: 1995.2.6. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) --- Series of Lectures --- "Free random variables and von Neumann algebras" Who: Prof. Kenneth J. Dykema (The Fields Institute) When: Feb 13(Mon) through Feb 18(Sat), 10:00 am Where: 27-414 What: Voiculescu's theory of freeness in noncommutative probability theory is a fundamental development. It's application to operator algebras has already yielded new knowledge about von Neumann algebras related to free groups. The talks will cover (1) the definition of freeness and examples (2) additive and multiplicative free convolution (3) freeness in random matrices (4) applications of freeness to von Neumann algebras, (we will briefly review needed facts about von Neumann algebras). More detailed information is available from Professor Sa Ge Lee (02-880-6542). -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.7 date: 19953.8. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1995.3 10. Fri 10:00 Jeong Ja A (Kyung Hee Univ.) Purely infinite simple C*-crossed products -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.8 date: 1995.3.14. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1995.3.17. Fri 10:00 Jeong Ja A (Kyung Hee Univ.) Classification of simple C*-algebras Several lectures are to be continued on the same topic every Friday. Main references are M. Rordam, Classification of certain infinite simple C*-algebras G. Elliott and M. Rordam, Classification ....., II M. Rordam, Classification ......., III G. Elliott's several papers on "classifications of simple C*-algebras" are also useful. -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.9 date: 1995.3.17. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1995.3.24. Fri 10:00 Kye Seung-Hyeok (Seoul National Univ.) A review on K-theory for C*-algebras, I 1995.3.31. Fri 10:00 Kye Seung-Hyeok (Seoul National Univ.) A review on K-theory for C*-algebras, II 1995.4.7. Fri 10:00 Cho Sung-Je (Seoul National Univ.) A review on Extension theory for C*-algebras -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.10 date: 1995.4.10. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1995.4.14. Fri 10:00 Cho Sung-Je (Seoul National Univ.) A review on Extension theory for C*-algebras, II -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.11 date: 1995.4.18. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1995.4.21. Fri 10:00 Cho Sung-Je (Seoul National Univ.) A review on Extension theory for C*-algebras, III -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.12 date: 1995.4.21. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1995.4.28. Fri 10:00 Kye Seung-Hyeok (Seoul National Univ.) Fourier and Fourier-Stieltjes algebras 1995.5.12. Fri 10:00 Jeong Ja A (Kyung Hee Univ.) KK-theory for C*-algebras, I 1995. 5.19 Fri 10:00 Jeong Ja A (Kyung Hee Univ.) KK-theory for C*-algebras, II 1995. 5.26 Fri 10:00 Jeong Ja A (Kyung Hee Univ.) KK-theory for C*-algebras, III ****** Jensen and Thomsen's "Elements of KK-theory" is a useful reference for KK-theory. ****** -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.13 date: 1995.8.23. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) We resume operator algebra seminar on September 15, after Chuseok holidays. Anybody who wants to talk, please let me know (O.880-6535/6531, H.595-0942). 1995.9.15 Fri 10:00 Sa-Ge Lee (Seoul National Univ.) On $n$-state spaces -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.14 date: 1995.9.6. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) Professor P. A. Fillmore, the President of the Canadian Mathematical Society, will visit Korea on the invitation of Korean Mathematical Society around the KMS meeting at Pusan. He will give talks in our seminar and SNU Math Colloquium. Here are tentative titles of his talks. "Classification of C*-algebras" at Sogang Univ. and SNU Colloquium "Structure of Matrix Bands" at SNU Operator Algebra Seminar "Operator K-theory" at KMS meeting "Noncommutative Topology" at Cheju University *************************************** 1995.9.15. Fri 10:00 Seung-Hyeok Kye (Seoul National Univ.) On the convex set of completely positive linear maps in matrix algebras 1995.9.15. Fri 4:00 (SNU Colloquium) Sa-Ge Lee (Seoul National Univ.) The *-isomorphism between unital C*-algebras descibed by generalized state space 1995.9.22. Fri 10:00 Sa-Ge Lee (Seoul National Univ.) On n-state spaces 1995.10.12. Thu 4:00 (SNU Colloquium) P. A. Fillmore (Dalhousie Univ.) Classification of C*-algebras 1995.10.13. Fri 10:00 P. A. Fillmore (Dalhousie Univ.) Structure of matrix bands -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.15 date: 1995.9.22. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1995.9.29. Fri 10:00 Shin Dongyun (Seoul City Univ.) Norms for Schur products 1995.10.6. Fri 10:00 Heo Jaeseong (Seoul National Univ.) Hilbert C*-modules and G. N. S. constructions for completely positive linear maps 1995.10.12. Thu 4:00 (SNU Colloquium) P. A. Fillmore (Dalhousie Univ.) Classification of C*-algebras 1995.10.13. Fri 10:00 P. A. Fillmore (Dalhousie Univ.) Structure of matrix bands 1995.10.20. Fri We may go on a hiking. 1995.10.27. Fri 10:00 Jang Sun Young (Ulsan Univ.) Reduced C*-crossed products by semigroups of automorphisms -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.16 date: 1995.11.29. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) We apologize for missing OPERATOR NEWS during two months by the trouble of the Department Machine. The seminar on this friday, December 1, has been cancelled. 1995.12.8. Fri 10:00 Park, Chun-Gil (Univ. of Maryland) The structure of tensor products of non-commutative tori with UHF-algebra and Cuntz algebra We report here the previous seminar which has not been announced. 1995.11.3. Fri 10:00, 27-411 Kye, Seung-Hyeok (Seoul National Univ.) Boundaries of the cone of positive linear maps and its subcones in matrix algebras -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.17 date: 1995.12.11. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1995.12.15. Fri 10:00 Lee, Sa-Ge (Seoul National Univ.) Multistates and normal multistates -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.18 date: 1995.12.20. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1995.12.28. Thu 10:00 Park, Chungil Twisted group C*-algebras and non-commutative tori, I 1995.12.29. Fri 10:00 Park, Chungil Twisted group C*-algebras and non-commutative tori, II 1996.1.5. Fri 10:00 somebody Twisted group C*-algebras and non-commutative tori, III -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.19 date: 1996.3.5. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) We resume operator algebra seminar on March 15. Anybody who wants to talk, please let me know (O.880-6535/6531, H.595-0942). 1996.3.15. Fri 10:00 Jeong, Ja A (Kyung Hee Univ.) Extremally rich C*-algebras and crossed products 1996.3.22. Fri 10:00 Kim, Sang Og (Hallym Univ.) Homotopy of projections in C*-algebras 1996.3.29. Fri 10:00 Lee, Sa-Ge (Seoul Nat'l Univ.) The M_\infty-bimodule associated with a unital C*-algebra -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.20 date: 1996.3.18. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) **** OPERATOR THEORY AND OPERATOR ALGEBRAS**** *** A Special Session of The Spring KMS Meeting *** when: 1996.4.26. 2:00 pm where:Chungnam National University, Taejeon ---- Part I: Chairman, Sa Ge Lee (Seoul National University) ---- 2:00 -- 2:40 Woo Young Lee (Sung Kyun Kwan University) Browder's theorem and Riesz points 2:40 -- 3:20 Il Bong Jung (Kyungpook National University) Quadratically hyponormal weighted shifts with the first two flats 3:20 -- 4:00 Dong Wan Park (Keimyung University) Limits algebras of stationary systems ---- Part II: Chairman, Young Soo Jo (Keimyung University) ---- 4:30 -- 5:10 Jeong Hee Hong (Korea Maritime University) Composition of subfactors and related Hopf algebras \cr 5:10 -- 5:50 Ja A Jeong (Kyung Hee University) On extremally rich crossed products \cr Detailed information will be appear in forthcoming Newsletter of KMS. -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.21 date: 1996.3.25. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.3.29. Fri 10:00 Lee, Sa-Ge (Seoul Nat'l Univ.) The M_\infty-bimodule associated with a unital C*-algebra 1996.4.12. Fri 10:00 Park, Chun-Gil (Seoul Nat'l Univ., GARC) Strong Morita equivalence for non-commutative tori 1996.4.19. Fri 10:00 Park, Chun-Gil (Seoul Nat'l Univ., GARC) Principal PU(k)-bundles over compact manifolds **** OPERATOR THEORY AND OPERATOR ALGEBRAS**** *** A Special Session of The Spring KMS Meeting *** when: 1996.4.26. 2:00 pm where:Chungnam National University, Taejeon ---- Part I: Chairman, Sa Ge Lee (Seoul National University) ---- 2:00 -- 2:40 Woo Young Lee (Sung Kyun Kwan University) Browder's theorem and Riesz points 2:40 -- 3:20 Il Bong Jung (Kyungpook National University) Quadratically hyponormal weighted shifts with the first two flats 3:20 -- 4:00 Dong Wan Park (Keimyung University) Limits algebras of stationary systems ---- Part II: Chairman, Young Soo Jo (Keimyung University) ---- 4:30 -- 5:10 Jeong Hee Hong (Korea Maritime University) Composition of subfactors and related Hopf algebras \cr 5:10 -- 5:50 Ja A Jeong (Kyung Hee University) On extremally rich crossed products \cr Detailed information will be appear in forthcoming Newsletter of KMS. -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.22 date: 1996.4.29. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.5.10. Fri 10:00 Jeong, Ja A (Kyung Hee Univ.) On approximately divisible C*-algebras 1996.5.17. Fri 10:00 Park, Chun-Gil (Seoul Nat'l Univ., GARC) $k$-homogeneous C*-algebras over compact manifolds 1996 5.31 Fri 10:00 Kye, Seung-Hyeok (Seoul Nat'l Univ.) Kac algebras and their duals, I 1996 6.7. Fri 10:00 Kye, Seung-Hyeok (Seoul Nat'l Univ.) Kac algebras and their duals, II -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.23 date: 1996.6.24. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.6.26 Wed 10:00 D. R. Farenick (Univ. of Regina) Matricial convexity in operator algebras -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.24 date: 1996.6.25. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.6.26 Wed 11:00 D. R. Farenick (Univ. of Regina) Matricial convexity in operator algebras -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.25 date: 1996.9.13. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.9.13 Fri 10:00 Kil-Chan Ha (Seoul Nat'l Univ) Extremal Markov maps in matrix algebras -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.26 date: 1996.9.6. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.9.13 Fri 10:00 Kil-Chan Ha (Seoul Nat'l Univ) Extremal Markov maps in matrix algebras 1996.9.20 Fri 10:00 Ja A Jeong (Kyung Hee Univ.) Extremely rich C*-algebras -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.27 date: 1996.9.21. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.10.4. Fri 10:00 Dong-Yun Shin (Seoul City Univ.) On the operator spaces structures on Hilbert spaces -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.28 date: 1996.10.7. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.10.11. Fri 10:00 Seung-Hyeok Kye (Seoul National Univ.) Operator spaces and tensor products 1996.11.18. Fri 10:00 Sa Ge Lee (Seoul National Univ.) Construction of an opertor affine map from S_n(B) into S_n(B*C) 1996.11.1. Fri 10:00 Jeong Hee Hong (Korea Maritime Univ.) bimodules over subfactors -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.29 date: 1996.10.18. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) Professor Hiroyuki Osaka at Ryukyu University will be here from November 21 to November 28, and give three times 100 minutes lectures as follows: When: Nov 25 Fri 10:00, Nov 25 Fri 3:00 and Nov 26 Sat 9:00 Title: Introduction to the classification of purely infinite simple C*-algebras - Friendly approach to Kirchberg's classification Theorem - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentstyle{article} \begin{document} Title: Introduction to the classification of purely infinite simple C*-algebras - Friendly approach to Kirchberg's classification Theorem - Abstract: In this lecture we try to presnt the detail proof of the following Kirchberg's striking results ([1]), which is an affirmative answer to Elliott's conjecture in the case of 5-algebras (purely infinite simple, separable, unital C*-algebras): {\bf Theorem B}. If $A$ and $B$ are 5-algebras with $A = A^{st}$ and $B = B^{st}$, then for every KK-equivalence $z \in KK(A,B)$ there exists a unital *-homomorphism $h$ from $A$ onto $B$ which induces the equivalent KK-element to $z$, where $A^{st}$ denotes the Cuntz standard form, that is, the $K_0$-element $[1_A]_0$ is a zero element in $K_0(A)$. As a corollary we get {\bf Corollary}. (1) Let $B$ be a simple seprable unital nuclear. Then, $$ B \otimes O_2 \cong O_2. $$ (2) Let $A$ be a simple separable unital nuclear. Then, $A$ is purely infinite if and only if $A \cong A \otimes O_\infty$. \vskip 5mm Note that we can get Corollary (1) directly in some sence not using Theorem B, if we use Elliott's elaborate result : $O_2 \otimes O_2 \cong O_2$.( R\o rdam presented the simple proof of it [3]) The point of the classification theory of Kirchberg is the usage of the following characterizaion of exact C*-algebras by him: {\bf Theorem A}. A separable C*-algebra $A$ is isomorphic to a C*-subalgebra of $O_2$ if and only if $A$ is exact. \vskip 5mm In this lecture, first of all, we will present the proof of Theorem A. The lecture note [4] should be useful for understanding it. After that, we will present a Kirchberg's abelian semigroup (discrete version), and give a proof of Corollary (1). Theorem A will play an important role in this abelian semigroup. Finally, we will present the outline of the proof of Theorem B. \begin{thebibliography}{99} \bibitem{} E. Kirchberg, {\it The classification of purely infinite simple C*-algebras using Kasparov's theory}, 3rd draft (94). \bibitem{} H. Osaka, {\it Introduction to the classification of purely infinite simple C*-algebras}, in preparation. \bibitem{} M. R\o rdam, {\it A simple proof of Elliott's result $O_2 = O_2 \cong O_2$}, C. R. Math. Rep. Acad. Sci. Canada 16(1994), 31 - 36. \bibitem{} S. Wassermann, {\it Exact C*-algebras and related topics}, Lecture notes Series, No.19, Global Analysis Research Center, Seoul National University, 1994. \end{thebibliography} \end{document} -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.30 date: 1996.10.25. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.11.1. Fri 10:00 Jeong Hee Hong (Korea Maritime Univ.) bimodules over subfactors ** Professor Osaka's lecture schedule should be corrected as follows: 1996.11.22. Fri 10:00 Hiroyuki Osaka (Ryukyu Univ.) Introduction to the classification of purely infinite simple C*-algebras, I - Friendly approach to Kirchberg's classification Theorem - 1996.11.22. Fri 3:00 Hiroyuki Osaka (Ryukyu Univ.) Introduction to the classification of purely infinite simple C*-algebras, II - Friendly approach to Kirchberg's classification Theorem - 1996.11.23. Sat 9:00 Hiroyuki Osaka (Ryukyu Univ.) Introduction to the classification of purely infinite simple C*-algebras, III - Friendly approach to Kirchberg's classification Theorem - -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.31 date: 1996.11.1. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.11.8. Fri 10:00 Jeong Hee Hong (Korea Maritime Univ.) Kac algebras arising from subfactors 1996.11.15. Fri 10:00 Seung-Hyeok Kye (Seoul National Univ.) Reviews on exact C*-algebras 1996.11.15. Fri 11:00 Ja A Jeong (Kyung Hee Univ.) Reviews on purely infinite C*-algebras ** The above two talks will cover preliminaries for Osaka's lecture. 1996.11.22. Fri 10:00 Hiroyuki Osaka (Ryukyu Univ.) Introduction to the classification of purely infinite simple C*-algebras, I - Friendly approach to Kirchberg's classification Theorem - 1996.11.22. Fri 3:00 Hiroyuki Osaka (Ryukyu Univ.) Introduction to the classification of purely infinite simple C*-algebras, II - Friendly approach to Kirchberg's classification Theorem - 1996.11.23. Sat 9:00 Hiroyuki Osaka (Ryukyu Univ.) Introduction to the classification of purely infinite simple C*-algebras, III - Friendly approach to Kirchberg's classification Theorem - -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.32 date: 1996.11.8. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.11.15. Fri 10:00 Seung-Hyeok Kye (Seoul National Univ.) Reviews on exact C*-algebras 1996.11.15. Fri 11:00 Ja A Jeong (Kyung Hee Univ.) Reviews on purely infinite C*-algebras ** The above two talks will cover preliminaries for Osaka's lecture. 1996.11.22. Fri 10:00 Hiroyuki Osaka (Ryukyu Univ.) Introduction to the classification of purely infinite simple C*-algebras, I - Friendly approach to Kirchberg's classification Theorem - 1996.11.22. Fri 3:00 Hiroyuki Osaka (Ryukyu Univ.) Introduction to the classification of purely infinite simple C*-algebras, II - Friendly approach to Kirchberg's classification Theorem - 1996.11.23. Sat 9:00 Hiroyuki Osaka (Ryukyu Univ.) Introduction to the classification of purely infinite simple C*-algebras, III - Friendly approach to Kirchberg's classification Theorem - 1996.11.29. Fri 10:00 Hyun Jae Yoo (Yonsei Univ.) Dirichlet operators for Gibbs measures on loop spaces -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.33 date: 1996.11.25. edited by Seung-Hyeok Kye (kye@math.snu.ac.kr) 1996.11.29. Fri 10:00 Hyun Jae Yoo (Yonsei Univ.) Dirichlet operators for Gibbs measures on loop spaces 1996.12.6. Fri 10:00 Hyunhye Shin (Yonsei Univ.) Generalized quantum Markov chain and dynamical entropy -------------------------------------------------------------------------------- ****** OPERATOR NEWS ***** No.34 date: 199?.??.??. edited by Jaeseong Heo (hjs@math.snu.ac.kr) 1996.11.29. Fri 10:00 Hyun Jae Yoo (Yonsei Univ.) Dirichlet operators for Gibbs measures on loop spaces 1996.12.6. Fri 10:00 Hyunhye Shin (Yonsei Univ.) Generalized quantum Markov chain and dynamical entropy