Distinguished Visiting Professor Talk: Il Bong Jung 2/23 @ 4 pm in Olin 372

Title:  Weighted shifts on directed trees

Abstract: 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 Hilbert space operators, which we propose to call weighted shifts on directed trees. We have studied the structure of these operators since 2012 and obtained some remarkable results about those operators. In this talk we discuss some of the established properties for such operators, for examples, normality, hyponormality, and subnormality, etc. It is well-known that the subnormality of Hilbert space operators is closely related to Stieltjes moment sequences. We consider directed trees with one branching vertex and establish a connection between the subnormality and Stieltjes moment sequences by using the k-step backward extendability of bounded subnormal weighted shifts. In addition, some exotic examples of weighted shifts on directed trees related to Stieltjes moment sequences are discussed.

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