## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

### Criteria of existence of bounded approximate identities in topological algebras

#### 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