Taylor and Xia spectra of \(p\)-hyponormal \(n\)-tuples
type: Item
instance of: scholarly article
title: Taylor and Xia spectra of \(p\)-hyponormal \(n\)-tuples
zbMATH Open document ID: 0962.47008
DOI: 10.1007/BF01232739
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 \(0< p\leq 1\) if \((T^*T)^p\geq (TT^*)^p\). In the case where \(p= 1\) we say simply that \(T\) is hyponormal. By using the Berberian extension theorem for an operator, the author proves the following: If \((A_1,\dots, A_n)\) is an \(n\)-tuple of doubly commuting \(p\)-hyponormal operators, then there is an \(n\)-tuple \((T_1,\dots, T_n)\) of doubly commuting hyponormal operators associated with \((A_1,\dots, A_n)\) such that \((A_1,\dots, A_n)\) and \((T_1,\dots, T_n)\) have the same Taylor spectra and Xia spectra. And, a an application of this, he generalizes the result given by Cho-Curto-Huruya-Zelazko for a Putnam area inequality of above \((T_1,\dots, T_n)\) to the case of \((A_1,\dots, A_n)\).
reviewed by: Takashi Yoshino
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47A30
zbMATH DE Number: 1484694
zbMATH Keywords: Berberian extension theorem
zbMATH Keywords: \(n\)-tuple
zbMATH Keywords: \(p\)-hyponormal operators
zbMATH Keywords: Taylor spectra
zbMATH Keywords: Xia spectra
zbMATH Keywords: Putnam area inequality
author: B. P. Duggal
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01232739
OpenAlex ID: W2329897844
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description: scientific article; zbMATH DE number 1484694