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Generalized spectrum and commuting compact perturbations

1993
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Proceedings of the Edinburgh Mathematical Society
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Let X be an infinite-dimensional complex Banach space and denote the set of bounded (compact) linear operators on X by B(X) (K(X)). Let N(A) and R(A) denote, respectively, the null space and the range space of Let a g (A) = C\{XeC:R(A -X) is closed and k{A -X) = 0} denote the generalized (regular) spectrum of A. In this paper we study the subset a gb (A) of <s g (A) defined by o gb (A) = C\{XeC:R(A -X) is closed and k(A -A)<oo}. Among other things, we prove that if / is a function analytic in a

doi:10.1017/s0013091500018332
fatcat:bojv7mv2gvc5lm6itknpieaooa