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Representation of locally convex algebras.

L. Oubbi — 1994

Revista Matemática de la Universidad Complutense de Madrid

We deal with the representation of locally convex algebras. On one hand as subalgebras of some weighted space CV(X) and on the other hand, in the case of uniformly A-convex algebras, as inductive limits of Banach algebras. We also study some questions on the spectrum of a locally convex algebra.

Reflexivity of spaces of weakly summable sequences.

L. OubbiM. A. Ould Sidaty — 2007

RACSAM

We deal with the space of Λ-summable sequences from a locally convex space E, where Λ is a metrizable perfect sequence space. We give a characterization of the reflexivity of Λ(E) in terms of that of Λ and E and the AK property. In particular, we prove that if Λ is an echelon sequence space and E is a Fréchet space then Λ(E) is reflexive if and only if Λ and E are reflexive.

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