Polaroid type operators and compact perturbations
Volume 221 / 2014
Studia Mathematica 221 (2014), 175-192
MSC: Primary 47A10; Secondary 47A55, 47A53.
DOI: 10.4064/sm221-2-5
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 $\varepsilon>0$, 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.
