A new class of sequence spaces with applications in summability theory.
In this paper we introduce a new sequence space defined by a sequence of Orlicz functions and study some topological properties of this sequence space.
In a previous work (1990) we introduced a certain property (y) on locally convex spaces and used it to remove the assumption of separability from the theorem of Bellenot and Dubinsky on the existence of nuclear Köthe quotients of Fréchet spaces. Our purpose is to examine condition (y) further and relate it to some other normability conditions. Some of our results were already announced in Önal (1989).
It is proved that if are separable quasi-Banach spaces, then contains a dense dual-separating subspace if either or has this property.