Publication: The Arens product in locally convex algebras. (Spanish: El Producto de Arens en álgebras localmente convexas).
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1976
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Real Academia de Ciencias Exactas, Físicas y Naturales
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Abstract
The author considers locally convex algebras. He defines an Arens product for such algebras and applies it to obtain various generalizations of results known for Banach algebras. He gives a necessary and sufficient condition for the existence of an approximate identity and, for a locally convex algebra with an approximate right identity, he gives a necessary and sufficient condition for the existence of a right identity. He shows that an element x≠0 is a right topological divisor of zero if and only if it is a right divisor of zero when considered as an element of the bidual space.
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M. Altman.1972.Contracteurs dans les algebres de Banach C.R.Acad.Ser.Paris,Ser.A-B 274,399-400.
R. Arens. 1951. The adjoint of a bilinear operation. Proc. Amer. Math. Soc., 2, 839-848.
F.F.Bonsall y J.Duncan.1973.Complete normed algebras.Springer-Verlag, Berlin.
M. M. Day.1973. Normed linear spaces. 3.a ed. Springer-Verlag, Berlín.
J.Horvath.1966.Topological vector spaces and distributions. Addison-Wesley Pub. Co. Reading, Massachusetts.
H.H.Schaefer.1971.Topological vector spaces. 3.a ed. Sprinber-Verlag, Berlin.
W.Zelazko.1973.Banach algebras. Elsevier Pub. Co. Amsterdam