Simple proof of the \(p\)-hyponormality of the Aluthge transformation
type: Item
instance of: scholarly article
title: Simple proof of the \(p\)-hyponormality of the Aluthge transformation
zbMATH Open document ID: 0929.47014
DOI: 10.1007/BF01233967
author: K. Appert
published in: Integral Equations and Operator Theory
publication date: 2000-01-25T00:00:00Z
review text: Let \({\mathcal H}\) be a complex Hilbert space and \({\mathcal B}({\mathcal H})\) be the set of all bounded linear operators on \({\mathcal H}\). An operator \(T\in{\mathcal B}({\mathcal H})\) is said to be \(p\)-hyponormal if \((T^*T)^p\geq (TT^*)^p\) \((p>0)\). For \(T\in{\mathcal B}({\mathcal H})\) with polar decomposition \(T= U| T|\) and for any \(s\) and \(t\) such as \(s\geq 0\) and \(t\geq 0\), the operator \(T(s,t)=| T|^s U| T|^t\) is called Aluthge transform of \(T\). In this paper, the authors give a simple proof of the special case \((0< p\leq 1)\) of the result given by reviewer about what kind of \(p\)-hyponormality is preserved under the Aluthge transform.
reviewed by: Takashi Yoshino
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47A63
zbMATH DE Number: 1271377
zbMATH Keywords: polar decomposition
zbMATH Keywords: Aluthge transform
zbMATH Keywords: \(p\)-hyponormality
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01233967
OpenAlex ID: W2030882565
description: scientific article; zbMATH DE number 1271377