On the uniqueness of uniform norms and C*-norms

P. A. Dabhi, and H. V. Dedania. "On the uniqueness of uniform norms and C*-norms." Studia Mathematica 191.3 (2009): 263-270. <http://eudml.org/doc/284622>.

@article{P2009,
abstract = {We prove that a semisimple, commutative Banach algebra has either exactly one uniform norm or infinitely many uniform norms; this answers a question asked by S. J. Bhatt and H. V. Dedania [Studia Math. 160 (2004)]. A similar result is proved for C*-norms on *-semisimple, commutative Banach *-algebras. These properties are preserved if the identity is adjoined. We also show that a commutative Beurling *-algebra L¹(G,ω) has exactly one uniform norm if and only if it has exactly one C*-norm; this is not true in arbitrary *-semisimple, commutative Banach *-algebras.},
author = {P. A. Dabhi, H. V. Dedania},
journal = {Studia Mathematica},
keywords = {commutative Banach algebra; commutative Banach -algebra; uniform norm; -norm; multiplier algebra; commutative Beurling algebra},
language = {eng},
number = {3},
pages = {263-270},
title = {On the uniqueness of uniform norms and C*-norms},
url = {http://eudml.org/doc/284622},
volume = {191},
year = {2009},
}

TY - JOUR
AU - P. A. Dabhi
AU - H. V. Dedania
TI - On the uniqueness of uniform norms and C*-norms
JO - Studia Mathematica
PY - 2009
VL - 191
IS - 3
SP - 263
EP - 270
AB - We prove that a semisimple, commutative Banach algebra has either exactly one uniform norm or infinitely many uniform norms; this answers a question asked by S. J. Bhatt and H. V. Dedania [Studia Math. 160 (2004)]. A similar result is proved for C*-norms on *-semisimple, commutative Banach *-algebras. These properties are preserved if the identity is adjoined. We also show that a commutative Beurling *-algebra L¹(G,ω) has exactly one uniform norm if and only if it has exactly one C*-norm; this is not true in arbitrary *-semisimple, commutative Banach *-algebras.
LA - eng
KW - commutative Banach algebra; commutative Banach -algebra; uniform norm; -norm; multiplier algebra; commutative Beurling algebra
UR - http://eudml.org/doc/284622
ER -