Characterization of Aluthge Transform of Composition Operators

Document Type : Original Article

Author
Morteza Sohrabi
Department of Mathematics, Lorestan University, Khorramabad, Iran.
10.22034/maco.2.1.3
Abstract
Let $widetilde{{C}_{varphi}}$ be the Aluthge transform of composition operator on $L^{2}(Sigma)$. The main result of this paper is characterizations of Aluthge transform of composition operators in some operator classes that are weaker than hyponormal, such as hyponormal, quasihyponormal, paranormal, $*$-paranormal on $L^{2}(Sigma)$. Moreover, to explain the results, we provide several useful related examples to show that $widetilde{{C}_{varphi}}$ lie between these classes. 

Keywords

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Mathematical Analysis and Convex Optimization
Volume 2, Issue 1
June 2021
Pages 29-38