On the uniqueness of uniform norms and C*-norms

• Autorzy: P. A. Dabhi , H. V. Dedania
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 22D15: Group algebras of locally compact groups
• 46K05: General theory of topological algebras with involution
• 46J05: General theory of commutative topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 191
• Numer: 3
• Strony: 263-270

Daty

wydano

2009

Twórcy

autor

P. A. Dabhi

• Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India

autor

H. V. Dedania

• Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India

Identyfikatory

DOI

10.4064/sm191-3-7