Bulletin of the Belgian Mathematical Society - Simon Stevin

On classifying involutive locally $m$-convex algebras, via cones

A. El Kinani, M. A. Nejjari, and M. Oudadess

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Abstract

We show that any hermitian $^{\ast}$-$l.m.c.a.$, the set of positive elements of which is a locally bounded cone, is necessarily a $Q$-algebra (the converse is not true). We also obtain that the algebra of complex numbers is the unique locally $C^{\ast}$-algebra without zero-divisors.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 4 (2006), 681-687.

Dates
First available in Project Euclid: 16 January 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1168957344

Digital Object Identifier
doi:10.36045/bbms/1168957344

Mathematical Reviews number (MathSciNet)
MR2300624

Zentralblatt MATH identifier
1134.46026

Subjects
Primary: 46H05: General theory of topological algebras
Secondary: 46K05: General theory of topological algebras with involution

Keywords
$m$-convex algebra hermitian algebra $Q$-algebra locally bounded cone zero-divisors

Citation

El Kinani, A.; Nejjari, M. A.; Oudadess, M. On classifying involutive locally $m$-convex algebras, via cones. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 4, 681--687. doi:10.36045/bbms/1168957344. https://projecteuclid.org/euclid.bbms/1168957344


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