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RESEARCH PRODUCT

Weyl Type Theorems for Left and Right Polaroid Operators

Pietro AienaEdixon BalzanElvis Aponte

subject

Teoremi di Weyl operatori polaroidi SVEPLeft and rightPure mathematicsAlgebra and Number TheorySpectrum (functional analysis)Banach spaceType (model theory)Bounded operatorAlgebraIsolated pointSettore MAT/05 - Analisi MatematicaAnalysisResolventMathematics

description

A bounded operator defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. In this paper we consider the two related notions of left and right polaroid, and explore them together with the condition of being a-polaroid. Moreover, the equivalences of Weyl type theorems and generalized Weyl type theorems are investigated for left and a-polaroid operators. As a consequence, we obtain a general framework which allows us to derive in a unified way many recent results, concerning Weyl type theorems (generalized or not) for important classes of operators.

yearjournalcountryeditionlanguage
2010-01-01Integral Equations and Operator Theory
https://doi.org/10.1007/s00020-009-1738-2