Domain of Binomial Matrix in Some Spaces of Double Sequences

Abstract

The target of the existing paper is to acquaint the new spaces B r,s ∞ , B r,s , B r,s bp and B r,s reg which consist of all double sequences whose binomial-transforms are in the spaces Mu, Cp, Cbp and Cr, respectively. Besides these, some properties of them are investigated and inclusion relations are given. Moreover, the α−, β(ϑ)− and γ−duals are determined. Finally, some 4-dimensional matrix mapping classes are characterized.