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Spectral analysis of non‐compact symmetrizable operators on Hilbert spaces
Author(s) -
MokhtarKharroubi Mustapha,
Mohamed Yahya
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3223
Subject(s) - mathematics , hilbert space , pure mathematics , complement (music) , eigenvalues and eigenvectors , spectrum (functional analysis) , operator (biology) , injective function , rigged hilbert space , essential spectrum , spectral properties , spectral theory , reproducing kernel hilbert space , biochemistry , chemistry , physics , computational chemistry , repressor , quantum mechanics , complementation , transcription factor , gene , phenotype
This paper revisits and complement in different directions the classical work by W. T. Reid on symmetrizable completely continuous transformations in Hilbert spaces and a more recent paper by one of the authors. More precisely, we deal with spectral properties of % non‐compact operators G on a complex Hilbert space H such that SG is self‐adjoint where S is a ( not necessarily injective) nonnegative operator. We study the isolated eigenvalues of G outside its essential spectral interval and provide variational characterization of them as well as stability estimates. We compare them also to spectral objects of S G . Finally, we characterize the Schechter essential spectrum of strongly symmetrizable operators in terms singular Weyl sequences; in particular, we complement J. I. Nieto's paper on the essential spectrum of symmetrizable. Copyright © 2014 John Wiley & Sons, Ltd.
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