Bicircular projections on some Banach spaces
type: Item
instance of: scholarly article
title: Bicircular projections on some Banach spaces
zbMATH Open document ID: 1123.47017
published in: Linear Algebra and its Applications
publication date: 2007-02-14T00:00:00Z
review text: Let \(X\) be a complex Banach space and \(T\in{\mathfrak B}(X)\). The operator \(T\) is said to be Hermitian if \(e^{i\theta T}\) is an isometry for every \(\theta\in\mathbb{R}\). Also, a projection \(P\) on \(X\) is a bicircular projection if \(e^{i\theta} P+ e^{i\beta}(I- P)\) is an isometry for all real values of \(\alpha\) and \(\beta\). The main result of the paper is as follows. Theorem. A projection on a complex Banach space is a bicircular projection if and only if it is a Hermitian projection. Finally, some immediate consequences of this result are proved.
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 5126048
zbMATH Keywords: bicircular projections
zbMATH Keywords: Hermitian operators
author: James Jamison
reviewed by: Bahmann Yousefi
MaRDI profile type: Publication
full work available at URL: j.laa.2006.05.009
OpenAlex ID: W2023299938
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DOI: 10.1016/J.LAA.2006.05.009
description: scientific article; zbMATH DE number 5126048