On invertibility of combinations of \(k\)-potent operators
type: Item
instance of: scholarly article
title: On invertibility of combinations of \(k\)-potent operators
zbMATH Open document ID: 1250.47001
author: Dragana Cvetković-Ilić
author: Chunyuan Deng
author: Yimin Wei
published in: Linear Algebra and its Applications
publication date: 2012-05-14T00:00:00Z
review text: A bounded linear operator \(P\) on a complex Hilbert space \(H\) is called \(k\)-potent if \(P^k=P\), where \(k \geq 2\). Let \(P_1,P_2\) be non-zero \(k\)-potents on \(H\). The authors study certain properties of operators of the form \(c_1P_1+c_2P_2-c_3P_1^sP_2^{k-1-s}\), where \(c_1,c_2\) and \(c_3\) are complex numbers, \(k\) is a positive integer, \(k \geq 2\) and \(s \leq k-1\). Questions concerning the invertibility and generalized invertibility of these operators are also studied.
reviewed by: K. C. Sivakumar
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 6034536
zbMATH Keywords: inverse
zbMATH Keywords: group inverse
zbMATH Keywords: linear combination of \(k\)-potents
MaRDI profile type: Publication
full work available at URL: j.laa.2012.02.011
OpenAlex ID: W2013024195
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DOI: 10.1016/J.LAA.2012.02.011
description: scientific article; zbMATH DE number 6034536