Polaroid type operators and compact perturbations

Chun Guang Li ¹   ; Ting Ting Zhou ²

¹ School of Mathematics and Statistics Northeast Normal University Changchun 130024, P.R. China
² Institute of Mathematics Jilin University Changchun 130012, P.R. China

Studia Mathematica, Tome 221 (2014) no. 2, pp. 175-192

Résumé

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 $\varepsilon>0$, there exists a compact operator $K$ with $\|K\|\varepsilon$ such that $T+K$ is polaroid. Moreover, we characterize those operators for which a certain polaroid type property is stable under (small) compact perturbations.

Détail

DOI : 10.4064/sm221-2-5

Keywords: bounded linear operator acting hilbert space said polaroid each isolated point spectrum pole resolvent there several generalizations polaroid property investigate compact perturbations polaroid type operators prove given operator varepsilon there exists compact operator varepsilon polaroid moreover characterize those operators which certain polaroid type property stable under small compact perturbations