2017년도 이전 세미나
I: Moment problems and operators, II: On weighted shifts on directed trees
|Category||2016 Fall Math Colloquium|
|날짜||2016-11-18||시간||15:50:00 ~ 18:00:00|
|장소||Math Sci Bldg 404||Host||Yun Sung Choi|
|Speaker||Il Bong Jung||소속||Kyungpook National University|
|TOPIC||I: Moment problems and operators, II: On weighted shifts on directed trees|
|소개 및 안내사항||Title I: Moment problems and operators
In 1894 T. Stieltjes introduced the moment problem with sequences of nonnegative real numbers as data, which is called Stieltjes moment problemnow. According to the associated moment measure and data, moment problems are given their terms classied in this topic; for example, Hamburger moment problem, Hausdor⁄ moment problem, complex moment problem, etc. The moment problem is closely related to some topics in operator theory and matrix theory. In this talk we discuss the following subjects.
What is the moment problem?
Relationships among moment problems, matrices and operators.
Recent aspects in the study of moment problems.
Title II: On weighted shifts on directed trees
The main goal of this research is to implement some methods of graph theory into operator theory. We do it by introducing a new class of (not necessarily bounded) operators, which we propose to call weighted shifts on directed trees. We discuss some fundamental properties of such operators. The relationships between domains of a weighted shift on a directed tree and its adjoint are described well. And normal-ity, hyponormality, cohyponormality and subnormality of such operators are entirely characterized in terms of their weights and directed trees. Moreover, a new method of verifying the subnormality of unbounded Hilbert space operators based on an ap-proximation technique is proposed. In particular, we consider directed trees with one branching vertex and establish a connection of the subnormality with k-step backward extendability of bounded subnormal weighted shifts. In addition, some interesting ex-amples of weighted shifts on directed trees related to Stieltjes moment sequences are discussed.