Bulletin of the Belgian Mathematical Society - Simon Stevin

Criteria of existence of bounded approximate identities in topological algebras

Christina P. Podara

Full-text: Open access

Abstract

Some results and criteria of existence concerning bounded approximate identities in Banach algebras are extended to the topological algebras setting. We thereby prove that the bidual of a commutative locally C*-algebra with either of the two Arens products is a unital commutative algebra, and that a quasinormable Fréchet m-convex algebra has a left (resp. right) bounded approximate identity if and only if it can be represented as an inverse limit of Banach algebras each of which has a left (resp. right) bounded approximate identity.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 5 (2010), 949-960.

Dates
First available in Project Euclid: 14 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1292334069

Digital Object Identifier
doi:10.36045/bbms/1292334069

Mathematical Reviews number (MathSciNet)
MR2777784

Zentralblatt MATH identifier
1214.46029

Subjects
Primary: 46H20: Structure, classification of topological algebras
Secondary: 46A20: Duality theory 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 46K05: General theory of topological algebras with involution 46M18: Homological methods (exact sequences, right inverses, lifting, etc.) 46M40: Inductive and projective limits [See also 46A13]

Keywords
Approximate identity/units topological algebra quasinormable Fréchet m-convex algebra bidual of a locally convex algebra Arens products Arens regularity

Citation

Podara, Christina P. Criteria of existence of bounded approximate identities in topological algebras. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 5, 949--960. doi:10.36045/bbms/1292334069. https://projecteuclid.org/euclid.bbms/1292334069


Export citation