Spectral mapping framework
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.
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.
Jaroslav Zemánek (1982)
Banach Center Publications
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Mohamed Barraa, Mohamed Boumazgour (2001)
Studia Mathematica
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We give a simple proof of the relation between the spectra of the difference and product of any two idempotents in a Banach algebra. We also give the relation between the spectra of their sum and product.
Saworotnow, P.P. (2003)
International Journal of Mathematics and Mathematical Sciences
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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].
M. Mathieu, G. J. Schick (2002)
Studia Mathematica
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A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is defined to be spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ Mr(x) for all x ∈ E, where r(·) denotes the spectral radius. We study some basic properties of this class of operators, which are sometimes analogous to, sometimes very different from, those of bounded operators between Banach spaces.
Litvinov, G.L. (2005)
Zapiski Nauchnykh Seminarov POMI
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Al-Moajil, Abdullah H. (1982)
International Journal of Mathematics and Mathematical Sciences
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T. Mouton, H. Raubenheimer (1993)
Studia Mathematica
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We give a spectral characterisation of rank one elements and of the socle of a semisimple Banach algebra.
Vladimír Müller (1977)
Commentationes Mathematicae Universitatis Carolinae
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Jaroslav Zemánek (1977)
Studia Mathematica
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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...
Peter Šemrl (2007)
Banach Center Publications
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The set of all bounded linear idempotent operators on a Banach space X is a poset with the partial order defined by P ≤ Q if PQ = QP = P. Another natural relation on the set of idempotent operators is the orthogonality relation defined by P ⊥ Q ⇔ PQ = QP = 0. We briefly survey known theorems on maps on idempotents preserving order or orthogonality. We discuss some related results and open problems. The connections with physics, geometry, theory of automorphisms, and linear preserver...