학술저널
LOCAL SPECTRAL PROPERTIES OF QUASI-DECOMPOSABLE OPERATORS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 29, No. 4
-
2016.11543 - 552 (10 pages)
- 2
In this paper we investigate the local spectral proper-ties of quasidecomposable operators. We show that if T ∈ L(X) is quasi-decomposable, then T has the weak-SDP and σ loc (T ) = σ(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 σ(T ), then T ∈ L(X) is quasi-decomposable if and only if f (T ) is quasi-decomposable. Finally, if T ∈ L(X) and S ∈ L(Y ) are asymptotically similar, then T is quasi-decomposable if and only if S does.
1. Introduction and basic definitions
2. Results
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