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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Exemples séparant certaines classes d'algèbres topologiques


Authors: Z. Abdelali and M. Chidami
Journal: Proc. Amer. Math. Soc. 129 (2001), 1763-1767
MSC (1991): Primary 46J05; Secondary 46J40
Published electronically: December 13, 2000
MathSciNet review: 1814108
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Abstract:

Esterle (1979) and Zelazko (1996 and 1990) gave an example of an algebra which cannot be topologized as a topological algebra (with jointly continuous multiplication), and Müller (in 1991) showed that there exists a topological algebra, which is indeed a locally bounded algebra, which cannot be topologized as a locally convex algebra.

To complete this study on the separation between the classes of algebras, we construct for every $p\in ]0,1]$ a locally bounded algebra which is $q$-normed for every $q\in ]0, \frac{p}{p+2}[$ which cannot be topologized as a locally $p$-convex algebra, and we deduce an example of a locally pseudoconvex algebra which cannot be topologized as a locally $p$-convex algebra for every $p\in ]0,1]$. We also show the existence of a topological algebra which cannot be topologized as a locally pseudoconvex algebra.


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Additional Information

Z. Abdelali
Affiliation: Département de Mathématiques, Univérsité Mohammed V, Faculté des Sciences, B.P 1014 Rabat, Maroc
Email: zinelab@hotmail.com

M. Chidami
Affiliation: Département de Mathématiques, Univérsité Mohammed V, Faculté des Sciences, B.P 1014 Rabat, Maroc
Email: chidami@fsr.ac.ma

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05685-9
PII: S 0002-9939(00)05685-9
Received by editor(s): December 11, 1998
Received by editor(s) in revised form: May 24, 1999, and October 1, 1999
Published electronically: December 13, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society