Projections as averages of isometries on minimal norm ideals
type: Item
instance of: scholarly article
title: Projections as averages of isometries on minimal norm ideals
zbMATH Open document ID: 1232.47019
author: James Jamison
author: Fernanda Botelho
published in: Linear Algebra and its Applications
publication date: 2011-07-15T00:00:00Z
review text: In the article under review, the authors consider projections on minimal norm ideals of \(B(H)\) (the space of all bounded operators on a Hilbert space \(H\)) that are represented as the average of two surjective isometries. More precisely, they describe projections of the form \(P(T)=\frac{A_1 T B_1 + A_2 T B_2}{2}\) for all \(T \in \mathcal{I}\) (\(\mathcal{I}\) being a minimal norm ideal of \(B(H)\)), where \(A_1,A_2,B_1\) and \(B_2\) are unitary operators satisfying the commutativity conditions \(A_1 A_2=A_2 A_1\) and \(B_1 B_2=B_2 B_1\). They also characterize classes of projections of the form \(P(T)= \frac{AT + T^t B}{2}\) and \(P(T)=\frac{AT^t + T^t B}{2}\), with \(A\) and \(B\) being unitary operators satisfying certain spectral conditions, respectively.
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 5924544
zbMATH Keywords: projections
zbMATH Keywords: average of isometries
zbMATH Keywords: ideals of operators
zbMATH Keywords: generalized bi-circular projections
reviewed by: Carsten Michels
MaRDI profile type: Publication
full work available at URL: j.laa.2011.03.019
OpenAlex ID: W1976441432
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DOI: 10.1016/J.LAA.2011.03.019
description: scientific article; zbMATH DE number 5924544