Generalized projections in Banach algebras
type: Item
instance of: scholarly article
title: Generalized projections in Banach algebras
zbMATH Open document ID: 1165.46026
author: Christoph Schmoeger
published in: Linear Algebra and its Applications
publication date: 2008-12-12T00:00:00Z
review text: Let \({\mathcal J}(A)\) be the set of all elements of the form \(a=h+ik\), where \(h\) and \(k\) are Hermitian elements in a complex unital Banach algebra \(A\) and \(i\) is the imaginary unit. The involution \(*\) on \({\mathcal J}(A)\) is defined by \((h+ik)^*=h-ik\). An element \(a\in{\mathcal J}(A)\) is a generalized projection if \(a^2=a^*\). The author states and proves some properties of generalized projections. He also finds some sufficient and some both sufficient and necessary conditions under which an element from \({\mathcal J}(A)\) is a generalized projection. In the last section, some of these results are generalized for the case of \(q\)-generalized projections for \(q\in\mathbb N\) and \(q>1\), i.e., for elements \(a\in{\mathcal J}(A)\) such that \(a^q=a^*\).
reviewed by: Mart Abel
Mathematics Subject Classification ID: 46K99
Mathematics Subject Classification ID: 46H99
zbMATH DE Number: 5382402
zbMATH Keywords: generalised projection
zbMATH Keywords: Hermitian element
zbMATH Keywords: normal element
zbMATH Keywords: complex unital Banach algebra
zbMATH Keywords: \(q\)-generalized projection
MaRDI profile type: Publication
full work available at URL: j.laa.2008.07.020
OpenAlex ID: W2041127443
cites work: Hermitian Projections and Orthogonality in Banach Spaces
cites work: Q5608364
cites work: The spectral characterization of generalized projections
cites work: Generalized and hypergeneralized projectors
cites work: A note on \(k\)-generalized projections
cites work: A Note on Hermitian Elements of a Banach Algebra
cites work: Q5667036
DOI: 10.1016/J.LAA.2008.07.020
description: scientific article; zbMATH DE number 5382402