Distinguished Visiting Professor Talk: Il Bong Jung 2/28 @ 4 pm in Olin 372

Title:  Quasinormality and weak quasinormality of operators


Abstract:  There are two notions to define the quasinormality of unbounded operators by Kaufman and Stochel-Szafraniec respectively. Our results show that Kaufman’s definition of an unbounded quasinormal operator coincides with that given by Stochel-Szafraniec. In this talk we discuss various characterizations of unbounded quasinormal operators. Examples demonstrating the sharpness of our results are constructed. An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. This approach establishes a new definition to be called weakly quasinormal operators. Some characterizations concerning to the weakly quasinormal operators are discussed. In addition, various examples and counterexamples illustrating the concepts of this work are constructed by using weighted shifts on directed trees.

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