Fredholm properties of the difference of orthogonal projections in a Hilbert space
type: Item
instance of: scholarly article
title: Fredholm properties of the difference of orthogonal projections in a Hilbert space
zbMATH Open document ID: 1082.47009
author: J. J. Koliha
author: Vladimir Rakočević
published in: Integral Equations and Operator Theory
publication date: 2005-06-15T00:00:00Z
review text: Let \(P\) and \(Q\) be orthogonal projections on an infinite-dimensional complex Hilbert space. The main result of this paper gives four conditions equivalent to \(P-Q\) being a Fredholm operator; for example, the essential norm (i.e., the distance to the compact operators) of \(P+Q-I\) being strictly less than \(1\), or \(P+Q\) and \(I-PQ\) being Fredholm operators. Moreover, explicit formulas for the Moore--Penrose inverse and for a Fredholm inverse of \(P-Q\) are given. Here \(S\) is a Fredholm inverse of \(T\) when \(I-ST\) and \(I-TS\) are finite rank operators.
Mathematics Subject Classification ID: 47A53
zbMATH DE Number: 2176182
zbMATH Keywords: Fredholm operator
zbMATH Keywords: Moore--Penrose inverse
zbMATH Keywords: Hilbert space orthogonal projection
reviewed by: M. González
MaRDI profile type: Publication
full work available at URL: s00020-003-1274-4
OpenAlex ID: W2018802517
DOI: 10.1007/S00020-003-1274-4
description: scientific article; zbMATH DE number 2176182