Extension d'un théorème de von Neumann dans les a*-algèbres.
Entire functions and equicontinuity of power maps in Baire algebras.
We obtain that the power maps are equicontinuous at zero in any Baire locally convex algebra with a continuous product in which all entire functions operate; whence is m-convex in the commutative case. As a consequence, we get the same result of Mityagin, Rolewicz and Zelazko for commutative B-algebras.
Harmonic functions operating in Hermitian Banach algebras.
The purpose of this paper is to introduce a harmonic functional calculus in order to generalize some extended versions of theorems of von Neumann, Heinz and Ky Fan.
Fonctions analytiques de contractions topologiques dans les algèbres hermitiennes.
In this paper we define a functional calculus, for harmonic vector valued functions, in Banach algebras with continuous involution. Using this calculus, we generalize in two settings the results of Shih and Tan on analytic functions of topological proper contractions to analytic vector valued functions in Hermitian Banach algebras. We also make an extension of other results such as Schwarz's lemma and Pick's theorem.
Equicontinuity of power maps in locally pseudo-convex algebras
We show that, in any unitary (commutative or not) Baire locally pseudo-convex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras.
Caracterisations des C*-algèbres par le calcul fonctionnel.
We prove that C*-algebras for an equivalent norm are the involutive Banach algebras which admit the continuous functional calculus.
Caracterisations de certaines algèbres de Banach par le calcul fonctionnel
We show that the Banach algebras with continuous involution are the Banach algebras which admit a harmonic functional calculus, while we prove that the hermitian commutative Banach algebras are exactly the involutive commutative Banach algebras that admit a real analytic functional calculus.
Almost commutative -seminormed -algebras. (-algèbres -semi-normées presque commutatives.)
On some von Neumann topological algebras.
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