A bounded linear operator T acting on a Hilbert space is said to be polaroid if each isolated point in the spectrum is a pole of the resolvent of T. There are several generalizations of the polaroid property. We investigate compact perturbations of polaroid type operators. We prove that, given an operator T and ε > 0, there exists a compact operator K with ||K|| < ε such that T + K is polaroid. Moreover, we characterize those operators for which a certain polaroid type property is stable under (small) compact perturbations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-2-5,
author = {Chun Guang Li and Ting Ting Zhou},
title = {Polaroid type operators and compact perturbations},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {175-192},
zbl = {1335.47008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-2-5}
}
Chun Guang Li; Ting Ting Zhou. Polaroid type operators and compact perturbations. Studia Mathematica, Tome 223 (2014) pp. 175-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-2-5/