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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.
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 -