Trace and determinant in Jordan-Banach algebras.

Bernard Aupetit; Abdelaziz Maouche

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Displaying similar documents to “Trace and determinant in Jordan-Banach algebras.”

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

$k$ -Bessel functions associated to a 3-rank Jordan algebra.

Dib, Hacen (2005)

International Journal of Mathematics and Mathematical Sciences

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Invertibility-preserving maps of $C^{*}$ -algebras with real rank zero.

Kovacs, Istvan (2005)

Abstract and Applied Analysis

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On isomorphisms of standard operator algebras

Lajos Molnár (2000)

Studia Mathematica

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We show that between standard operator algebras every bijective map with a certain multiplicativity property related to Jordan triple isomorphisms of associative rings is automatically additive.

Analytic properties of the spectrum in Banach Jordan Systems.

Gerald Hessenberger (1996)

Collectanea Mathematica

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For Banach Jordan algebras and pairs the spectrum is proved to be related to the spectrum in a Banach algebra. Consequently, it is an analytic multifunction, upper semicontinuous with a dense G delta-set of points of continuity, and the scarcity theorem holds.

Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems

Gareth Braatvedt, Rudolf Brits, Francois Schulz (2015)

Studia Mathematica

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As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.

Recent trends in the field of Jordan-Banach algebras

Bernard Aupetit (1994)

Banach Center Publications

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On quasinilpotent equivalence of finite rank elements in Banach algebras

Heinrich Raubenheimer (2010)

Czechoslovak Mathematical Journal

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We characterize elements in a semisimple Banach algebra which are quasinilpotent equivalent to maximal finite rank elements.

The set of automorphisms of B(H) is topologically reflexive in B(B(H))

Lajos Molnár (1997)

Studia Mathematica

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The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence $(Φ_{n})$ of automorphisms of B(H) (depending on A) such that $Φ (A) = l i m_{n} Φ_{n} (A)$ . Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).

On rank one and finite elements of Banach algebras

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.

On rank one elements

Robin Harte (1995)

Studia Mathematica

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Without the "scarcity lemma", two kinds of "rank one elements" are identified in semisimple Banach algebras.