[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2016.29.4.543

LOCAL SPECTRAL PROPERTIES OF QUASI-DECOMPOSABLE OPERATORS

Yoo, Jong-Kwang (Department of Liberal Arts and Science Chodang University)
Oh, Heung Joon (Department of Liberal Arts and Science Chodang University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.29, no.4, 2016 , pp. 543-552 More about this Journal

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.

Keywords

local spectral theory; quasi-decomposable; perturbations; SVEP;

Citations & Related Records

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