LOCAL SPECTRAL PROPERTIES OF QUASI-DECOMPOSABLE OPERATORS

Abstract

In this paper we investigate the local spectral properties of quasidecomposable operators. We show that if T 2 L(X) is quasi-decomposable, then T has the weak-SDP and (cid:27)loc(T ) = (cid:27)(T ): Also, we show that the quasi-decomposability is preserved under commuting quasi-nilpotent perturbations. Moreover, we show that if f : U ! C is an analytic and injective on an open neighborhood U of (cid:27)(T ); then T 2 L(X) is quasi-decomposable if and only if f (T ) is quasi-decomposable. Finally, if T 2 L(X) and S 2 L(Y ) are asymptotically similar, then T is quasi-decomposable if and only if S does.

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