Open AccessA New Identity for Resolvents of Operators
Author(s) -
Michael I. Gil’
Publication year - 2013
Publication title -
international journal of analysis
Language(s) - English
Resource type - Journals
eISSN - 2314-4998
pISSN - 2314-498X
DOI - 10.1155/2013/243891
Subject(s) - mathematics , identity (music) , pure mathematics , operator theory , spectral theorem , spectrum (functional analysis) , algebra over a field , hilbert space , physics , quantum mechanics , acoustics
A new identity for resolvents of operators is suggested. We show that in appropriatesituations it is more convenient than the Hilbert identity. In particular, we establish a newinvertibility condition for perturbed operators as well as new bounds for the spectrum ofperturbed operators. As a particular case we consider perturbations of Hilbert-Schmidtoperators
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