P-convexity of Musielak-Orlicz sequence spaces of Bochner type.
We prove that in the Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, P-convexity coincides with reflexivity.
In this paper, denotes a complete, non-trivially valued, non-archimedean field. Sequences and infinite matrices have entries in The main purpose of this paper is to prove some product theorems involving the methods and in such fields
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.
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.