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Sonja Mouton (2014)
Studia Mathematica
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We apply Aupetit's scarcity theorem to obtain stronger versions of many spectral-theoretical results in ordered Banach algebras in which the algebra cone has generating properties.
Rudi Brits (2011)
Studia Mathematica
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We extend an example of B. Aupetit, which illustrates spectral discontinuity for operators on an infinite-dimensional separable Hilbert space, to a general spectral discontinuity result in abstract Banach algebras. This can then be used to show that given any Banach algebra, Y, one may adjoin to Y a non-commutative inessential ideal, I, so that in the resulting algebra, A, the following holds: To each x ∈ Y whose spectrum separates the plane there corresponds a perturbation of x, of...
S. Mouton (2006)
Studia Mathematica
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Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least...
Jaroslav Zemánek (1977)
Studia Mathematica
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Jaroslav Zemánek (1982)
Banach Center Publications
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Anar Dosiev (2005)
Banach Center Publications
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In this paper we suggest a general framework of the spectral mapping theorem in terms of parametrized Banach space bicomplexes.
Vlastimil Pták (1982)
Banach Center Publications
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Vladimír Müller (1977)
Commentationes Mathematicae Universitatis Carolinae
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H. du T. Mouton, S. Mouton (2002)
Studia Mathematica
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We recall from [9] the definition and properties of an algebra cone C of a real or complex Banach algebra A. It can be shown that C induces on A an ordering which is compatible with the algebraic structure of A. The Banach algebra A is then called an ordered Banach algebra. An important property that the algebra cone C may have is that of normality. If C is normal, then the order structure and the topology of A are reconciled in a certain way. Ordered Banach algebras have interesting...
P. A. Cojuhari, A. M. Gomilko (2008)
Studia Mathematica
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The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.
Zemánek, Jaroslav
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Tosio Kato (1982)
Mathematische Zeitschrift
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Laura Burlando (1994)
Banach Center Publications
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This survey deals with necessary and/or sufficient conditions for continuity of the spectrum and spectral radius functions at a point of a Banach algebra.
A. Sołtysiak (2002)
Studia Mathematica
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An example is given of a semisimple commutative Banach algebra that has the strong spectral extension property but fails the multiplicative Hahn-Banach property. This answers a question posed by M. J. Meyer in [4].