A formula for gap between two closed operators
type: Item
instance of: scholarly article
title: A formula for gap between two closed operators
zbMATH Open document ID: 1193.47003
author: S. H. Kulkarni
author: G. Ramesh
published in: Linear Algebra and its Applications
publication date: 2010-04-29T00:00:00Z
review text: Let \(H_1\) and \(H_2\) are Hilbert spaces and \(A,B\in B(H_1,H_2)\). Then the gap between \(A\) and \(B\) is defined as the gap between the corresponding graphs \(G(A)\) and \(G(B)\), i.e., \( \theta(A,B)=\|P_{G(A)}-P_{G(B)}\|\). \textit{J.\,Faghih-Habibi} [Linear Algebra Appl.\ 186, 55--57 (1993; Zbl 0773.15011)] computed a formula for \(\theta(A,0)\), where \(A\) is an \(m\times n\) matrix. \textit{R.\,Nakamoto} [Math.\ Jap.\ 42, No.\,2, 219--232 (1995; Zbl 0842.47007)] generalized Habibi's formula for bounded operators \(A,B\in B(H_1,H_2)\). In the paper under review, the authors extend the results of these papers to the case of densely defined unbounded closed operators.
reviewed by: Maryam Amyari
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 5702842
zbMATH Keywords: densely defined operator
zbMATH Keywords: closed operator
zbMATH Keywords: graph of an operator
zbMATH Keywords: square root of an operator
zbMATH Keywords: gap of an operator
zbMATH Keywords: gap between operators
MaRDI profile type: Publication
full work available at URL: j.laa.2010.01.004
OpenAlex ID: W1972262745
cites work: Q4877167
cites work: Q5526483
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cites work: Spectral methods for linear inverse problems with unbounded operators
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cites work: Functional Operators (AM-22), Volume 2
DOI: 10.1016/J.LAA.2010.01.004
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description: scientific article; zbMATH DE number 5702842