Displaying similar documents to “Fonctions harmoniques opérant sur les algèbres de Banach involutives”

Fonctions analytiques de contractions topologiques dans les algèbres hermitiennes.

Abdellah El Kinani (1990)

Collectanea Mathematica

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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.

Caracterisations de certaines algèbres de Banach par le calcul fonctionnel

A. Akkar, Abdellah El Kinani, M. Oudadess (1989)

Extracta Mathematicae

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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.