◾ Overview: Recently, there has been active interaction among function theory and operator theory. This mini-workshop aims to share an opportunity for intensive open debate and interaction on Toeplitz and Hankel operators.

◾ Date: July 16-19, 2025

◾ Venue: Gyeongsang National Univ 354-120

◾ Schedule:

[1] Caixing Gu’s lecture

Lecture 1: Almost invariance of kernels of perturbed operators

Abstract: In this lecture, we prove that if the kernel of a bounded linear operator A is almost invariant for the operator T, then the kernel of a finite rank perturbation of A is also almost invariant for the operator T. Furthermore, the defect spaces of these kernels are identified.

Lecture 2: Almost shift invariance of kernels of perturbed Toeplitz and Hankel operators

Abstract: In this lecture, we first present several results for the almost shift or backward shift invariances of kernel of Toeplitz and Hankel operators. We then apply the general theory from Lecture 1 to study these properties for finite rank perturbations of Toeplitz and Hankel operators. Effort is made to compute several explicit defect spaces.

[2] In Sung Hwang’s lecture

Lecture 1: Strongly measurable vector-valued functions

Abstract: In this lecture, we prove that if a vector-valued(Banach space-valued) function on the unit circle is measurable, then the function is essentially separably valued. Thus, by the Pettis’ measurability theorem, we have that every vector-valued measurable function is strongly measurable.

Lecture 2: Lusin’s theroem for vector-valued functions

Abstract: One of Littlewood's three principles says that every measurable function is nearly continuous. An example is Lusin's theorem. In this lecture, we give a separable Banach space-valued version of Lusin's theorem: Let X be a separable Banach space and f be a X-valued measurable function on the unit circle. Then f is nearly continuous.

◾ Organizers

In Sung Hwang (Sungkyunkwan Univ) 

Doobae Jun (Gyeongsang National Univ)

Woo Young Lee (KIAS)

Sunguk Yoo (Gyeongsang National Univ)

◾ Supported by:  Sungkyunkwan Univ, KIAS-HCMC, Gyeongsang National Univ, NRF-Korea

◾ Contact: Woo Young Lee (wylee@kias.re.kr), In Sung Hwang (ihwang@skku.edu)