해석학특강(작용소공간) 강의계획
(1999 년 2 학기)
담당교수:계승혁(27-428, 전화 880-6535, E-mail: kye at math.snu.ac.kr)
시간: 수3 (24-411), 금 2,3 (상산관 307호)
Every Banach space is a space of bounded functions on a suitable set,
and so Banach spaces are essentially "spaces of functions". An operator space V is, by definition, a subspace of the Banach space B(H) of all bounded linear operators on a Hilbert space H. Since B(H) is a non-commutative version of the space of bounded functions, an operator space is understood as a "non-commutative" or "quantized" version of a Banach space.
The space M_n(V) of all n by n matrices over an operator space V has a natural norm inherited from the identification M_n(B(H))=B(H^n) for each natural number n. These norms satisfy simple axioms, which characterize an abstract operator spaces. The theory of operator spaces was studied extensively during last ten years, and turned out to be useful to study operator algebra and noncommutative harmornic analysis.
In this lecture, we will study the basic notions of operator spaces, including Ruan's representation theorem, Arveson-Wittstock's extension theorem, dual construction, tensor products, approximation properties, exactness and local reflexivity.
The preliminary for this lecture is "elementary notion of Banach spaces", usually touched in Real Analysis Course (senior or first year graduate)