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On some vector valued sequence space using Orlicz function. (English) Zbl 0953.46002

The authors introduce the construction of a certain vector sequence space with the purpose of generalizing several constructions existing in the literature, such as Orlicz spaces, classical vector sequence spaces, etc. Their ingredients are: a sequence of Banach spaces \(E_k\), a normal sequence space \(F\) with monotone Schauder basis, and an Orlicz function \(M\). The definition of the space they call \(F(E_k, M)\) can be imagined by some. What they prove in the paper is that “the space \(F(E_k, M)\) turns out to be a complete normed space (…) Inclusion relations, separability, convergence criteria etc (…)”.

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
46A35 Summability and bases in topological vector spaces
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