Bulletin of the Belgian Mathematical Society - Simon Stevin

On different barrelledness notions in locally convex algebras

M. Haralampidou, M. Oudadess, L. Palacios, and C. Signoret

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Abstract

This is a synthetic presentation of several barrelledness notions, in locally convex algebras. These are characterized, as in locally convex spaces, via (algebra) seminorms. This approach reveals a new notion of barrelledness. The latter shows to be what is needed to have meaningful statements in locally uniformly convex algebras.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 1 (2015), 25-38.

Dates
First available in Project Euclid: 20 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1426856855

Digital Object Identifier
doi:10.36045/bbms/1426856855

Mathematical Reviews number (MathSciNet)
MR3325718

Zentralblatt MATH identifier
1328.46038

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

Keywords
Barrelled space $m$-barrelled algebra $m$-infrabarrelled algebra Mackey completeness locally uniformly $A$-convex algebra $Q$-algebra

Citation

Haralampidou, M.; Oudadess, M.; Palacios, L.; Signoret, C. On different barrelledness notions in locally convex algebras. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 1, 25--38. doi:10.36045/bbms/1426856855. https://projecteuclid.org/euclid.bbms/1426856855


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