Banach Journal of Mathematical Analysis

On some von Neumann topological algebras

Rachid Choukri, Abdellah El Kinani, and Mohamed Oudadess

Full-text: Open access

Abstract

We show that a regular von Neumann $Q$-$m$-convex Frechet algebra is of finite dimension. We also show that a regular von Neumann $m$-convex Frechet algebra is a projective limit of finite dimensional algebras. Finally, we prove that a bilateral $Q$-$F$-algebra is a regular von Neumann algebra if and only if it is isomorphic to a finite product of algebras which are also fields.

Article information

Source
Banach J. Math. Anal., Volume 3, Number 2 (2009), 55-63.

Dates
First available in Project Euclid: 17 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1261086709

Digital Object Identifier
doi:10.15352/bjma/1261086709

Mathematical Reviews number (MathSciNet)
MR2517299

Zentralblatt MATH identifier
1200.46038

Subjects
Primary: 46H05: General theory of topological algebras
Secondary: 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Keywords
Regular von Neumann $Q$-$m$-convex Frechet algebra bilateral $Q$-$F$-algebra topological algebra

Citation

Choukri, Rachid; El Kinani, Abdellah; Oudadess, Mohamed. On some von Neumann topological algebras. Banach J. Math. Anal. 3 (2009), no. 2, 55--63. doi:10.15352/bjma/1261086709. https://projecteuclid.org/euclid.bjma/1261086709


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