Spectral properties for some extensions of isometric operators
type: Item
instance of: scholarly article
title: Spectral properties for some extensions of isometric operators
zbMATH Open document ID: 1498.47022
author: D. Kharzeev
published in: Annals of Functional Analysis
publication date: 2020-07-17T00:00:00Z
review text: The author obtains some properties of \(2\)-isometric and quasi-\(2\)-isometric operators, shows that the spectrum is continuous on the set of all \(2\)-isometric operators and deduces that the Weyl and Browder spectrum have the same properties. He also proves that, if \(T , S^{*}\) are \(2\)-isometric and invertible isometric operators, respectively, and \(X\) is a Hilbert-Schmidt operator such that \(T X = X S\), then \(T^{*}X = X S^{*}\). Moreover, the author shows that every Riesz projection \(E\) of a \(2\)-isometric operator \(T \) is self-adjoint and satisfies \( \mathcal{R}(E) = \mathcal{N}(T -\lambda) = \mathcal{N} (T -\lambda)^{*}\), where \(\mathcal{N}(T), \mathcal{R}(T)\) denote the kernel and the range of \(T\in B(\mathcal{H})\), respectively. It is shown that a quasi-\(2\)-isometric operator satisfies Bishop's property (\(\beta\)). Finally, Weyl-type theorems are proved for \(f(d_{T,S})\), with quasi-\(2\)-isometric operator entries \(T\) and \(S^{*} \).
reviewed by: F. Lombarkia
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 7222415
zbMATH Keywords: 2-isometry
zbMATH Keywords: quasi-2-isometry
zbMATH Keywords: Riesz projection
zbMATH Keywords: Bishop's property (\(\beta\))
zbMATH Keywords: Weyl-type theorems
MaRDI profile type: Publication
full work available at URL: s43034-019-00043-y
OpenAlex ID: W3005231455
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DOI: 10.1007/S43034-019-00043-Y
description: scientific article; zbMATH DE number 7222415