\(\omega\)-hyponormal operators. II
type: Item
instance of: scholarly article
title: \(\omega\)-hyponormal operators. II
zbMATH Open document ID: 0962.47007
DOI: 10.1007/BF01194481
author: Ariyadasa Aluthge
author: Derming Wang
published in: Integral Equations and Operator Theory
publication date: 2001-06-18T00:00:00Z
review text: An operator \(T\) on a Hilbert space \({\mathcal H}\) is said to be \(p\)-hyponormal for \(p>0\) if \((T^*T)^p\geq (TT^*)^p\). By using Ando's result, it is known that every \(p\)-hyponormal operator is paranormal (i.e., \(\|Tx\|^2\leq\|T^2x\|\) \(\|x\|\) for all \(x\in{\mathcal H}\)). Let \(T= U|T|\) be the polar decomposition of \(T\). Then it is also known that every \(p\)-hyponormal operator \(T\) satisfies the condition \[ \bigl||T|^{{1\over 2}} U|T|^{{1\over 2}}\bigr|\geq |T|\geq \bigl||T|^{{1\over 2}} U^*|T|^{{1\over 2}}\bigr|.\tag{\(\sharp\)} \] In this paper, the authors call the operator \(T\) which satisfies the condition \((\sharp)\) is \(w\)-hyponormal and prove that every \(w\)-hyponormal operator is also paranormal. [For part I see ibid. 36, No. 1, 1-10 (2000; Zbl 0938.47021)].
reviewed by: Takashi Yoshino
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 47B15
zbMATH DE Number: 1523219
zbMATH Keywords: \(w\)-hyponormal operator
zbMATH Keywords: paranormal
zbMATH Keywords: \(p\)-hyponormal operator
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1523219