Closing the gap in a subspace perturbation bound
type: Item
instance of: scholarly article
title: Closing the gap in a subspace perturbation bound
zbMATH Open document ID: 0782.47014
DOI: 10.1016/0024-3795(93)90522-P
author: R. McEachin
published in: Linear Algebra and its Applications
publication date: 1994-02-24T00:00:00Z
review text: Let \(X\) and \(Y\) be bounded self-adjoint operators on a Hilbert space \(\mathcal H\) and \(K_ X\subseteq \sigma(X)\), \(K_ Y\subseteq \sigma(Y)\) closed sets bounded apart by \(\delta>0\) with corresponding spectral projectors \(E\) and \(F\). From the work [\textit{R. Bhatia}, \textit{C. Davis} and \textit{P. Koosis}, J. Funct. Anal. 82, 138-150 (1989; Zbl 0674.42002)] it is known that \({\pi\over 2}||| X-Y|||\geq \delta||| EF|||\) for any unitary invariant norm. In the article under review it is shown that \({\pi\over 2}\) is best possible in this equality. The analogous question for normal operators is discussed.
Mathematics Subject Classification ID: 47A55
zbMATH DE Number: 179131
zbMATH Keywords: self-adjoint operators
zbMATH Keywords: spectral projectors
zbMATH Keywords: perturbation bounds
zbMATH Keywords: unitary invariant norm
zbMATH Keywords: normal operators
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 179131