## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 19, Number 3 (2012), 473-483.

### $m$-infrabarrelledness and $m$-convexity

Marina Haralampidou and Mohamed Oudadess

#### Abstract

$m$-infrabarrelledness, in the context of locally convex algebras, is considered to prove results previously obtained for barrelled algebras. Thus, any unital commutative $m$-infrabarrelled advertibly complete and pseudo-complete locally $m$-convex algebra with bounded elements has the $Q$-property; hence, it is functionally continuous (: all characters are continuous). In the framework of commutative $GB^{\ast }$-algebras with jointly continuous multiplication and bounded elements, the notions {\em $m$-infrabarrelled algebra} and {\em $C^{\ast }$-algebra} coincide. In unital uniform locally $m$-convex algebras, $m$-infrabarrelledness is equivalent to the Banach algebra structure, modulo pseudo-completeness. Moreover, $m$-infrabarrelledness for locally $A$-convex algebras (in particular, $A$-normed ones) is also examined.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 3 (2012), 473-483.

**Dates**

First available in Project Euclid: 14 September 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1347642377

**Digital Object Identifier**

doi:10.36045/bbms/1347642377

**Mathematical Reviews number (MathSciNet)**

MR3027355

**Zentralblatt MATH identifier**

1268.46031

**Subjects**

Primary: 46H05: General theory of topological algebras 46H20: Structure, classification of topological algebras 46K05: General theory of topological algebras with involution

**Keywords**

Locally $m$-convex algebra locally $A$-convex algebra $m$-infrabarrelled algebra $Q$-algebra locally $C^*$-algebra $GB^*$-algebra

#### Citation

Haralampidou, Marina; Oudadess, Mohamed. $m$-infrabarrelledness and $m$-convexity. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 3, 473--483. doi:10.36045/bbms/1347642377. https://projecteuclid.org/euclid.bbms/1347642377