Generalized invertibility of operator matrices
type: Item
instance of: scholarly article
title: Generalized invertibility of operator matrices
zbMATH Open document ID: 1264.47001
author: Dragan S. Djordjević
author: Milica Z. Kolundžija
published in: Arkiv för Matematik
publication date: 2012-12-06T00:00:00Z
review text: Let \(Z\) be a Banach space, such that \(Z=X\oplus Y\) for some closed and complementary subspaces \(X\) and \(Y\). Then each operator \(M\in \mathbb B(Z)\) which is invariant on \(X\), has a decomposition into some operators \(A\in\mathbb B(X)\), \(B\in\mathbb B(Y)\) and \(C\in\mathbb B(Y, X)\). In this paper, the authors discuss under which conditions on \(A\) and \(B\), there exists some \(C\) such that \(M\) has a generalized inverse, or is left Browder (that is, left Fredholm with finite ascent), or has some other similar properties.
reviewed by: Maryam Khosravi
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A53
zbMATH DE Number: 6112908
zbMATH Keywords: operator on Banach space
zbMATH Keywords: generalized inverse
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: Fredholm operators
zbMATH Keywords: relatively regular spectrum
MaRDI profile type: Publication
full work available at URL: s11512-011-0152-6
OpenAlex ID: W2047930878
cites work: Browder essential approximate point spectra and hypercyclicity for operator matrices
cites work: Q4422033
cites work: Q3116319
cites work: Invertible completions of $2\times 2$ upper triangular operator matrices
cites work: \(a\)-Weyl's theorem for operator matrices
cites work: Weyl's theorem for operator matrices
cites work: Continuous spectrum, point spectrum and residual spectrum of operator matrices
DOI: 10.1007/S11512-011-0152-6
description: scientific article; zbMATH DE number 6112908