On Some Spaces Isomorphic to the Space of Absolutely q-summable Double Sequences

Abstract

Let 0 < q < infinity. In this study, we introduce the spaces BVq and LSq of q-bounded variation double sequences and q-summable double series as the domain of four-dimensional backward difference matrix Delta and summation matrix S in the space L-q of absolutely q-summable double sequences, respectively. Also, we determine their alpha- and beta-duals and give the characterizations of some classes of four-dimensional matrix transformations in the case 0 < q <= 1.