Unitary Banach algebras

Julio Becerra Guerrero, et al. "Unitary Banach algebras." Studia Mathematica 162.1 (2004): 25-51. <http://eudml.org/doc/284843>.

@article{JulioBecerraGuerrero2004,
abstract = {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.},
author = {Julio Becerra Guerrero, Simon Cowell, Ángel Rodríguez Palacios, Geoffrey V. Wood},
journal = {Studia Mathematica},
keywords = {unitary Banach algebra; unitary element; -algebra},
language = {eng},
number = {1},
pages = {25-51},
title = {Unitary Banach algebras},
url = {http://eudml.org/doc/284843},
volume = {162},
year = {2004},
}

TY - JOUR
AU - Julio Becerra Guerrero
AU - Simon Cowell
AU - Ángel Rodríguez Palacios
AU - Geoffrey V. Wood
TI - Unitary Banach algebras
JO - Studia Mathematica
PY - 2004
VL - 162
IS - 1
SP - 25
EP - 51
AB - 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.
LA - eng
KW - unitary Banach algebra; unitary element; -algebra
UR - http://eudml.org/doc/284843
ER -