Polaroid type operators under perturbations

Pietro Aiena, and Elvis Aponte. "Polaroid type operators under perturbations." Studia Mathematica 214.2 (2013): 121-136. <http://eudml.org/doc/285866>.

@article{PietroAiena2013,
abstract = {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.},
author = {Pietro Aiena, Elvis Aponte},
journal = {Studia Mathematica},
keywords = {localized SVEP; polaroid type operators; Weyl type theorems.},
language = {eng},
number = {2},
pages = {121-136},
title = {Polaroid type operators under perturbations},
url = {http://eudml.org/doc/285866},
volume = {214},
year = {2013},
}

TY - JOUR
AU - Pietro Aiena
AU - Elvis Aponte
TI - Polaroid type operators under perturbations
JO - Studia Mathematica
PY - 2013
VL - 214
IS - 2
SP - 121
EP - 136
AB - 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.
LA - eng
KW - localized SVEP; polaroid type operators; Weyl type theorems.
UR - http://eudml.org/doc/285866
ER -