Displaying similar documents to “On the defect spectrum of an extension of a Banach space operator”

On the topological boundary of the one-sided spectrum

Vladimír Müller (1999)

Czechoslovak Mathematical Journal

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It is well-known that the topological boundary of the spectrum of an operator is contained in the approximate point spectrum. We show that the one-sided version of this result is not true. This gives also a negative answer to a problem of Schmoeger.

Ascent spectrum and essential ascent spectrum

O. Bel Hadj Fredj, M. Burgos, M. Oudghiri (2008)

Studia Mathematica

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We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X has some finite rank power if and only if σ a s c e ( T + F ) = σ a s c e ( T ) for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued...

On a certain class of subspectra

Andrzej Sołtysiak (1991)

Commentationes Mathematicae Universitatis Carolinae

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The aim of this paper is to characterize a class of subspectra for which the geometric spectral radius is the same and depends only upon a commuting n -tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity.