Abstract
We show that the convexified topology of a locally pseuod-convex algebra can be determined by an explicit family of seminorms. A natural relationship between some properties of locally pseudo-convex algebras and the associated locally convex algebras obtained by convexification is also established.
Similar content being viewed by others
References
Abel M.,Strongly spectrally bounded algebras, Act. Comm. Univ. Tartuensis,899 (1990), 71–90.
El Kinani A., Chahboun M.,Convexifiée d’une topologie d’algèbre A-p-normée, Functiones et Approximatio, Comm. Math. Poznan,XXIX (2001), pp. 89–98.
Jarchow H.,Locally convex spaces, B.G. Teubner Stuttgart, 1981.
Lescarret C., Moreau J. J.,Convexifiée d’une topologie d’espace vectoriel topologique, Séminaire d’Analyse convexe -1- Montpellier (1971), 21–27.
Mallios A.,Topological algebras, Selected topics. North-Holland. 1986.
Le Page C.,Sur quelques conditions impliquant la commutativité dans les algèbres de Banach, C. R. A. S. Paris, Ser. A-B;265 (1967), A235-A237.
Xia Dao-Xing (Hsia. Tao-Hsing),On locally bounded topological algebras, Acta Math. Sinica 14 No 2 (1964). Engl. Ubers. Chinese-Math. 5 No 2 261–276. (1964).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
El Kinani, A. Convexification in locally pseudo-convex algebras. Rend. Circ. Mat. Palermo 53, 407–416 (2004). https://doi.org/10.1007/BF02875733
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02875733
Key words and phrases
- Locally pseudo-convex algebra
- convexification of linear topology
- Q-algebra
- advertibly complete algebra