On Certain Properties on Vector - Valued Sequence Space on Product Normed Space

Abstract

The notion of vector valued sequence space is a generalized form of spaces of scalar valued sequences, and its terms consist of sequences from a vector space. In this work, we shall study some conditions that characterize the linear space structures and containment relations of the space of sequences whose terms from a product normed space. The aim of this paper is to deal with   a vector valued sequence space 1∞ (A x B, || . || ,  ,ū ) with its terms from a product normed space A x B. We shall also investigate the linear space structure of 1∞(A x B, || . ||, ,ū ) with respect to  co-ordinatewise vector operations, the primary  interest is to explore the conditions in terms of   and  so that a class 1∞ ( A x B, || . ||,  ,ū )  is contained in or equal to another class of  the same kind.