On the Domain of Riesz Mean in the Space L-s*

WOS: 000397270800004Let 0 < s < infinity. In this study, we introduce the double sequence space R-qt(L-s) as the domain of four dimensional Riesz mean R-qt in the space L-s of absolutely s-summable double sequences. Furthermore, we show that R-qt(L s) is a Banach space and a barrelled space for 1 <= s < infinity and is not a barrelled space for 0 < s < 1. We determine the alpha- and beta(V)-duals of the space L-s for 0 < s <= 1 and fi (bp)-dual of the space R-qt(L-s) for 1 < s < 1, where # 2 f p; bp; r g. Finally, we characterize the classes (L-s : M-u), (L-s : C-bp), (R-qt(L-s) : M-u) and (R-qt(L-s) : C-bp) of four dimensional matrices in the cases both 0 < s < 1 and 1 <= s < 1 together with corollaries some of them give the necessary and su ffi cient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space