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Sharp Generalized Carleman Inequalities with Minimal Information about the Spectrum
Author(s) -
Dechevski Ljubomir T.,
Persson Lars Erik
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941680105
Subject(s) - mathematics , resolvent , spectrum (functional analysis) , hilbert space , norm (philosophy) , pure mathematics , operator (biology) , compact operator , quasinormal operator , separable space , discrete mathematics , finite rank operator , mathematical analysis , extension (predicate logic) , banach space , biochemistry , chemistry , physics , repressor , quantum mechanics , political science , transcription factor , computer science , law , gene , programming language
Abstract Let H and T: H → H denote a separable Hilbert space and an operator in a Schatten‐von Neumann ideal S p ( H ), respectively. Consider the resolvent operator (λ I ‐ T ) −1 , where I is the identity operator and λ belongs to the resolvent set of T . Some sharp bounds for the uniform operator norm of (λ I ‐ T ) −1 are derived in some situations of particular interest for certain applications, namely when only partial or minimal information about the spectrum is available. The results obtained may also be regarded as generalizations of Carleman's inequality for quasinilpotent operators.