Spectra of operators with Bishop’s property (𝛽)

Drissi, M.; El Hodaibi, M.; Zerouali, E.

doi:10.1090/S0002-9939-08-08947-8

Spectra of operators with Bishop’s property $(\beta )$
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by M. Drissi, M. El Hodaibi and E. H. Zerouali PDF

Proc. Amer. Math. Soc. 136 (2008), 1609-1617 Request permission

Abstract:

Let $X$ be a Banach space and let $\mathcal {A}(X)$ be the class that consists of all operators $T\in \mathcal {L}(X)$ such that for every $\lambda \in \mathbb {C}$, the range of $(T-\lambda I)$ has a finite-codimension when it is closed. For an integer $n\in \mathbb {N}$, we define the class $\mathcal {A}_{n}(X)$ as an extension of $\mathcal {A}(X)$. We then study spectral properties of such operators, and we extend some known results of multi-cyclic operators with $(\beta )$.

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