LOCAL SPECTRAL PROPERTIES OF QUASI-DECOMPOSABLE OPERATORS

다국어 초록 (Multilingual Abstract)

In this paper we investigate the local spectral properties of quasidecomposable operators. We show that if $T{\in}L(X)$ is quasi-decomposable, then T has the weak-SDP and ${\sigma}_{loc}(T)={\sigma}(T)$. Also, we show that the quasi-decomposability is preserved under commuting quasi-nilpotent perturbations. Moreover, we show that if $f:U{\rightarrow}{\mathbb{C}}$ is an analytic and injective on an open neighborhood U of ${\sigma}(T)$, then $T{\in}L(X)$ is quasi-decomposable if and only if f(T) is quasi-decomposable. Finally, if $T{\in}L(X)$ and $S{\in}L(Y)$ are asymptotically similar, then T is quasi-decomposable if and only if S does.