On New Space of Vector-Valued Generalized Bounded Sequences Defined on Product Normed Space

Abstract

Abstract:In this paper, we introduce and study a new vector valued sequence spacel( XY, –, u– ,|| . ||)with its terms from a product normed spaceXY. Beside investigating the linear space structure of l( X × Y, –, u–,|| . || ) with respect to co-ordinatewise vector operations, our primarily interest is to explore the conditions in terms of u–and–so thata class l( X × Y, –, u–,|| . || ) is contained in or equal to another class of same kind .

Keywords: Sequence space, Generalized sequence space, Product-normed space.