1Dipartimento di Metodi e Modelli Matematici Facoltà di Ingegneria Università degli Studi di Palermo I-90128 Palermo, Italy 2Departamento de Matemáticas Facultad de Ciencias UCLA Barquisimeto, Venezuela
Studia Mathematica, Tome 214 (2013) no. 2, pp. 121-136
A bounded operator $T$ defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. The “polaroid” condition is related to the conditions of being left polaroid, right polaroid, or $a$-polaroid. In this paper we explore all these conditions under commuting perturbations $K$. As a consequence, we give a general framework from which we obtain, and also extend, recent results concerning Weyl type theorems (generalized or not) for $T+K$, where $K$ is an algebraic or a quasi-nilpotent operator commuting with $T$.
Keywords:
bounded operator defined banach space said polaroid every isolated point spectrum pole resolvent polaroid condition related conditions being polaroid right polaroid a polaroid paper explore these conditions under commuting perturbations consequence general framework which obtain extend recent results concerning weyl type theorems generalized where algebraic quasi nilpotent operator commuting
Affiliations des auteurs :
Pietro Aiena
1
;
Elvis Aponte
2
1
Dipartimento di Metodi e Modelli Matematici Facoltà di Ingegneria Università degli Studi di Palermo I-90128 Palermo, Italy
2
Departamento de Matemáticas Facultad de Ciencias UCLA Barquisimeto, Venezuela
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author = {Pietro Aiena and Elvis Aponte},
title = {Polaroid type operators under perturbations},
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Pietro Aiena; Elvis Aponte. Polaroid type operators under perturbations. Studia Mathematica, Tome 214 (2013) no. 2, pp. 121-136. doi: 10.4064/sm214-2-2
