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The Generic Local Spectrum of Any Operator is The Full Spectrum
Author(s) -
Prunaru Bebe,
Putinar Mihai
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398005608
Subject(s) - mathematics , spectrum (functional analysis) , extension (predicate logic) , banach space , bounded operator , approximation property , bounded function , operator (biology) , tuple , pure mathematics , discrete mathematics , finite rank operator , mathematical analysis , transcription factor , gene , programming language , biochemistry , chemistry , physics , repressor , quantum mechanics , computer science
Let T =( T 1 , …, T n ) be a commuting n ‐tuple of bounded linear operators acting on some complex Banach space X. We show that if T has the single‐valued extension property, then the local spectrum σ T ( x ) coincides with the spectrum σ( T ), for all vectors x ∈ X, except on a set of the first Baire category. 1991 Mathematics Subject Classification 47A11, 47A13.