Integral Equations and Operator Theory

, Volume 66, Issue 1, pp 1–20

Weyl Type Theorems for Left and Right Polaroid Operators

Article

DOI: 10.1007/s00020-009-1738-2

Cite this article as:
Aiena, P., Aponte, E. & Balzan, E. Integr. Equ. Oper. Theory (2010) 66: 1. doi:10.1007/s00020-009-1738-2

Abstract

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.

Mathematics Subject Classification (2010)

Primary 47A10 47A11 Secondary 47A53 47A55 

Keywords

Localized SVEP semi B-Brower operators left and right Drazin invertibility Weyl’s theorem property (w

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Dipartimento di Metodi e Modelli Matematici, Facoltà di IngegneriaUniversità di PalermoPalermoItaly
  2. 2.Departamento de MatemáticasFacultád de Ciencias UCLABarquisimetoVenezuela
  3. 3.Departamento de Matemáticas, Facultád de CienciasUniversidad del ZuliaMaracaiboVenezuela

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