Polaroid type operators and compact perturbations

Volume 221 / 2014

Chun Guang Li, Ting Ting Zhou Studia Mathematica 221 (2014), 175-192 MSC: Primary 47A10; Secondary 47A55, 47A53. DOI: 10.4064/sm221-2-5


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.


  • Chun Guang LiSchool of Mathematics and Statistics
    Northeast Normal University
    Changchun 130024, P.R. China
  • Ting Ting ZhouInstitute of Mathematics
    Jilin University
    Changchun 130012, P.R. China

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