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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-2-2,
author = {Pietro Aiena and Elvis Aponte},
title = {Polaroid type operators under perturbations},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {121-136},
zbl = {1278.47007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-2-2}
}
Pietro Aiena; Elvis Aponte. Polaroid type operators under perturbations. Studia Mathematica, Tome 215 (2013) pp. 121-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-2-2/