On the stability of the spectral properties under commuting perturbations

Kai Yan  (Ph.D, Tongji University)

14:00 pm to 15:00 pm, May 13th, 2015   Science Building A1510

Abstract:

In this work, we examine the stability of several spectral properties under commuting perturbations. In particular, we show that if $T \in L(X)$ is an isoloid operator satisfying generalized Weyl's theorem and if $F \in L(X)$ is a power finite rank operator that commutes with $T$, then generalized Weyl's theorem holds for $T + F$. In addition, we consider the permanence of Bishop's property ($\beta$), at a point, under commuting perturbation that is an algebraic operator.

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