Ghosh, D.; Srivastava, P. D. On some vector valued sequence space using Orlicz function. (English) Zbl 0953.46002 Glas. Mat., III. Ser. 34, No. 2, 253-261 (1999). 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 (…)”. Reviewer: J.M.F.Castillo (Badajoz) Cited in 3 Documents MSC: 46A45 Sequence spaces (including Köthe sequence spaces) 46A35 Summability and bases in topological vector spaces Keywords:Orlicz spaces; vector sequence spaces; monotone Schauder basis; Orlicz function; inclusion relations; separability; convergence criteria PDFBibTeX XMLCite \textit{D. Ghosh} and \textit{P. D. Srivastava}, Glas. Mat., III. Ser. 34, No. 2, 253--261 (1999; Zbl 0953.46002)