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Totally convex algebras

Dieter Pumplün, Helmut Röhrl (1992)

Commentationes Mathematicae Universitatis Carolinae

By definition a totally convex algebra $A$ is a totally convex space $| A |$ equipped with an associative multiplication, i.eȧ morphism $μ : | A | \otimes | A | ⟶ | A |$ of totally convex spaces. In this paper we introduce, for such algebras, the notions of ideal, tensor product, unitization, inverses, weak inverses, quasi-inverses, weak quasi-inverses and the spectrum of an element and investigate them in detail. This leads to a considerable generalization of the corresponding notions and results in the theory of Banach spaces.

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

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.

Trace and determinant in Jordan-Banach algebras.

Bernard Aupetit, Abdelaziz Maouche (2002)

Publicacions Matemàtiques

Using an appropriate definition of the multiplicity of a spectral value, we introduce a new definition of the trace and determinant of elements with finite spectrum in Jordan-Banach algebras. We first extend a result obtained by J. Zemánek in the associative case, on the connectedness of projections which are close to each other spectrally (Theorem 2.3). Secondly we show that the rank of the Riesz projection associated to a finite-rank element a and a finite subset of its spectrum is equal to the...

Displaying 61 – 66 of 66

Totally convex algebras

Trace and determinant in Banach algebras

Trace and determinant in Jordan-Banach algebras.

Trace and Spectrum Preserving Linear Mappings in Jordan-Banach Algebras.

Traces on the cone algebra with asymptotics

Two-sided Banach algebras

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