|Date||Aug 17, 2022|
8월 16일(화) 1강: 14:00-17:00: Douglas-Shapiro-Shields factorizations
8월 17일(수) 2강: 14:00-17:00: Equivalence problems of Hankel operators
8월 18일(목) 3강: 14:00-17:00: Subnormality of Toeplitz operators
In this intensive lecture we consider the spectral theory of Hankel and Toeplitz operators with operator-valued symbols. In the first lecture, we consider meromorphic pseudo-continuation of bounded type functions and then discuss about a relationship between those functions and the Douglas-Shapiro-Shields factorization. In the second lecture we examine equivalence problems of Hankel operators related to the composition of a scalar inner function of degree d. In particular, this problem results in an equivalence of Toeplitz operators with such symbols. In the third lecture we consider the Halmos’ problem 5 for Toeplitz operators with operator-valued symbols. We focus at the operator-valued version of Abrahamse’s theorem. Moreover, in this version, we notice that we need the assumption - the symbol and the adjoint of the symbol have same pole. In particular, we recognize that this assumption is disappeared for the cases of rational functions.