On joint spectra of operators on a Banach space isomorphic to its square
Andrzej Sołtysiak (1989)
Colloquium Mathematicae
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Andrzej Sołtysiak (1989)
Colloquium Mathematicae
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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.
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 for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued...
V. Müller (1997)
Studia Mathematica
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We construct a pair of commuting Banach space operators for which the splitting spectrum is different from the Taylor spectrum.
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 -tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity.
W. Żelazko, Z. Słodkowski (1974)
Studia Mathematica
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