Classes of operators related to isometries
type: Item
instance of: scholarly article
title: Classes of operators related to isometries
zbMATH Open document ID: 1444.47037
author: Yanyan Li
published in: Advances in Operator Theory
publication date: 2020-04-24T00:00:00Z
review text: Let \(H\) be a complex Hilbert space and \(B(H)\) be the algebra of all bounded linear operators on \(H\). The authors define certain extensions of isometric operators. An operator \(T\in B(H)\) is said to be an analytic extension of an isometric operator if there exists an invariant subspace \(M\) such that \(T\vert_{M} \) is isometric and the restriction of \(T^{*} \) on \(M^{\bot} \) is algebraic. It is shown that, if \(T\) is an analytic extension of an isometric operator, then \(T\) is subscalar of order \(2n+2\); also, \(T\) satisfies Bishop's property (\(\beta\)), satisfies the single-valued extension property (SVEP), and is polaroid. Similar results are proved for operators which are \(F\)-quasi isometric. These are the operators \(T\) for which \(F(T)^{*} (T^{*} T-I)F(T)=0\) for some non-constant analytic function \(F\) defined on a neighbourhood of the spectrum \(\sigma (T)\).
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47A11
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 7193245
zbMATH Keywords: isometries
zbMATH Keywords: \(n\)-quasi-isometry
zbMATH Keywords: analytic extension of isometries
zbMATH Keywords: invariant subspace
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
full work available at URL: s43036-019-00029-6
OpenAlex ID: W2995028509
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DOI: 10.1007/S43036-019-00029-6
description: scientific article; zbMATH DE number 7193245