Integral Equations and Operator Theory

, Volume 66, Issue 1, pp 1–20

Weyl Type Theorems for Left and Right Polaroid Operators


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


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 


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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