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Product Theorems for Certain Summability Methods in Non-archimedean Fields

P.N. Natarajan (2003)

Annales mathématiques Blaise Pascal

In this paper, K denotes a complete, non-trivially valued, non-archimedean field. Sequences and infinite matrices have entries in K . The main purpose of this paper is to prove some product theorems involving the methods M and ( N , p n ) in such fields K .

Quasinormability of some spaces of holomorphic mappings.

José M. Isidro (1990)

Revista Matemática de la Universidad Complutense de Madrid

A class of locally convex vector spaces with a special Schauder decomposition is considered. It is proved that the elements of this class, which includes some spaces naturally appearing in infinite dimensional holomorphy, are quasinormable though in general they are neither metrizable nor Schwartz spaces.

Reflexivity of spaces of weakly summable sequences.

L. Oubbi, M. 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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