Polaroid type operators under perturbations

Pietro Aiena¹ ; Elvis Aponte²

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

Studia Mathematica, Tome 214 (2013) no. 2, pp. 121-136

Résumé

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 $T$.

Détail

DOI : 10.4064/sm214-2-2

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