Polaroid type operators and compact perturbations

Chun Guang Li, and Ting Ting Zhou. "Polaroid type operators and compact perturbations." Studia Mathematica 221.2 (2014): 175-192. <http://eudml.org/doc/285711>.

@article{ChunGuangLi2014,
abstract = {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.},
author = {Chun Guang Li, Ting Ting Zhou},
journal = {Studia Mathematica},
keywords = {polaroid operators; -polaroid operators; left and right polaroid operators; hereditarily polaroid operators; compact perturbations},
language = {eng},
number = {2},
pages = {175-192},
title = {Polaroid type operators and compact perturbations},
url = {http://eudml.org/doc/285711},
volume = {221},
year = {2014},
}

TY - JOUR
AU - Chun Guang Li
AU - Ting Ting Zhou
TI - Polaroid type operators and compact perturbations
JO - Studia Mathematica
PY - 2014
VL - 221
IS - 2
SP - 175
EP - 192
AB - 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.
LA - eng
KW - polaroid operators; -polaroid operators; left and right polaroid operators; hereditarily polaroid operators; compact perturbations
UR - http://eudml.org/doc/285711
ER -