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.
@article{urn:eudml:doc:42364,
title = {Fonctions analytiques de contractions topologiques dans les alg\`ebres hermitiennes.},
journal = {Collectanea Mathematica},
volume = {41},
year = {1990},
pages = {197-216},
mrnumber = {MR1163902},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42364}
}
El Kinani, Abdellah. Fonctions analytiques de contractions topologiques dans les algèbres hermitiennes.. Collectanea Mathematica, Tome 41 (1990) pp. 197-216. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42364/