Putnam's inequality for log-hyponormal operators
type: Item
instance of: scholarly article
title: Putnam's inequality for log-hyponormal operators
zbMATH Open document ID: 1062.47031
published in: Integral Equations and Operator Theory
publication date: 2004-03-07T00:00:00Z
review text: Let \(H\) be a complex Hilbert space and \(B(H)\) the algebra of all bounded linear operators on \(H\). An operator \(T\in B(H)\) is \(p\)-hyponormal if \((T^*T)^p\geq (TT^*)^p\). An operator \(T\in B(H)\) is log-hyponormal if \(T\) is invertible and \(\log(T^*T)\geq\log(TT^*)\) [see \textit{K. Tanahashi}, Integral Equations Oper. Theory 34, No. 3, 364--372 (1999; Zbl 0935.47015)]. In the present paper, the author proves Putnam's inequality for log-hyponormal operators, i.e., if \(T\) is log-hyponormal, then \[ \|\log(T^*T)- \log(TT^*)\|\leq{1\over \pi} \iint_{\sigma(T)} r^{-1}dr\,d\theta. \]
reviewed by: Eungil Ko
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 2051561
zbMATH Keywords: log-hyponormal operator
zbMATH Keywords: Putnam's inequality
author: Kotaro Tanahashi
MaRDI profile type: Publication
full work available at URL: s00020-999-1172-5
OpenAlex ID: W2375830205
DOI: 10.1007/S00020-999-1172-5
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description: scientific article; zbMATH DE number 2051561