Spectral decomposition of a Hilbert space by a Fredholm operator
type: Item
instance of: scholarly article
title: Spectral decomposition of a Hilbert space by a Fredholm operator
zbMATH Open document ID: 0662.47012
DOI: 10.1016/0022-1236(88)90026-2
author: John Locker
author: Patrick M. Lang
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: Given a Fredholm operator with countable spectrum in a Hilbert space, the authors characterize the possibility of decomposing the Hilbert space into a direct sum of all generalized eigenspaces and the intersection of the ranges of the corresponding iterated operators. This is a generalization of the well-known spectral decomposition with respect to finitely many poles. The main result says that such a decomposition is possible iff the sums of the spectral projections are uniformly bounded. The result is illustrated by a differential operator in \(L_ 2[0,1]\).
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47B40
Mathematics Subject Classification ID: 47A70
zbMATH DE Number: 4082344
zbMATH Keywords: Fredholm operator with countable spectrum in a Hilbert space
zbMATH Keywords: decomposing the Hilbert space into a direct sum of all generalized eigenspaces
zbMATH Keywords: spectral decomposition
reviewed by: Volker Wrobel
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90026-2
OpenAlex ID: W1964389692
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description: scientific article; zbMATH DE number 4082344