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Weyl's Theorem, a ‐Weyl's Theorem, and Local Spectral Theory
Author(s) -
Curto Raúl E.,
Han Young Min
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702004027
Subject(s) - mathematics , extension (predicate logic) , banach space , spectrum (functional analysis) , pure mathematics , property (philosophy) , unbounded operator , fixed point theorem , discrete mathematics , approximation property , physics , quantum mechanics , computer science , programming language , philosophy , epistemology
Necessary and sufficient conditions are given for a Banach space operator with the single‐valued extension property to satisfy Weyl's theorem and a ‐Weyl's theorem. It is shown that if T or T * has the single‐valued extension property and T is transaloid, then Weyl's theorem holds for f(T) for every f ∈ H (σ( T )). When T * has the single‐valued extension property, T is transaloid and T is a‐isoloid, then a‐Weyl's theorem holds for f(T) for every f ∈ H (σ( T )). It is also proved that if T or T * has the single‐valued extension property, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.