On joint spectra of operators on a Banach space isomorphic to its square
Andrzej Sołtysiak (1989)
Colloquium Mathematicae
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Displaying similar documents to “On the defect spectrum of an extension of a Banach space operator”
On joint spectra of operators on a Banach space isomorphic to its square
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 for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued...
The splitting spectrum differs from the Taylor spectrum
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.
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 -tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity.
On joint spectra of commuting families of operators
W. Żelazko, Z. Słodkowski (1974)
Studia Mathematica
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On the axiomatic theory of spectrum
V. Kordula, V. Müller (1996)
Studia Mathematica
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There are a number of spectra studied in the literature which do not fit into the axiomatic theory of Żelazko. This paper is an attempt to give an axiomatic theory for these spectra, which, apart from the usual types of spectra, like one-sided, approximate point or essential spectra, include also the local spectra, the Browder spectrum and various versions of the Apostol spectrum (studied under various names, e.g. regular, semiregular or essentially semiregular).