Aluthge transforms of weighted shifts on directed trees

2014/01/17 by Jacek Trepkowski, Trepkowski, Jacek · 1 citation
Mathematics · #47B20 #47B33 (Secondary) #47B37 (Primary) #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1401.4415

openalex publication_date 2014/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Aluthge transform of a bounded operator is generalized to the case of unbounded one. A formula for the Aluthge transform of a weighted shift on a directed tree is established and it is used to construct an example of a hyponormal operator whose Aluthge transform has trivial domain. It is proven that such an example can be also constructed in the class of composition operators. It is also shown that Aluthge transform of a closed, densely defined operator is not necessarily closable.

Cited by

• Weakly centered weighted composition operators in L²-spaces

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