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.
@article{urn:eudml:doc:38331,
title = {Caracterisations de certaines alg\`ebres de Banach par le calcul fonctionnel},
journal = {Extracta Mathematicae},
volume = {4},
year = {1989},
pages = {145-147},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38331}
}
Akkar, A.; El Kinani, Abdellah; Oudadess, M. Caracterisations de certaines algèbres de Banach par le calcul fonctionnel. Extracta Mathematicae, Tome 4 (1989) pp. 145-147. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38331/