In a Banach algebra an invertible element which has norm one and whose inverse has norm one is called unitary. The algebra is unitary if the closed convex hull of the unitary elements is the closed unit ball. The main examples are the C*-algebras and the ℓ₁ group algebra of a group. In this paper, different characterizations of unitary algebras are obtained in terms of numerical ranges, dentability and holomorphy. In the process some new characterizations of C*-algebras are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-1-3,
author = {Julio Becerra Guerrero and Simon Cowell and \'Angel Rodr\'\i guez Palacios and Geoffrey V. Wood},
title = {Unitary Banach algebras},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {25-51},
zbl = {1058.46028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-1-3}
}
Julio Becerra Guerrero; Simon Cowell; Ángel Rodríguez Palacios; Geoffrey V. Wood. Unitary Banach algebras. Studia Mathematica, Tome 162 (2004) pp. 25-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-1-3/