Duals of generalized Orlicz Hilbert sequence spaces and matrix transformations

Abstract

In this paper, we define the sequence spaces hc increment (m) v , M,u, p , h0 increment (m) v , M,u, p and h & INFIN; increment (m) v , M,u, p resulting from the infinite Hilbert matrix and the Musielak-Orlicz function. We give some topological prop-erties and inclusion relations of these newly created spaces. We also identified & alpha;-, & beta;- and & gamma;-duals of the spaces. Finally, we tried to characterize some matrix transformations between these spaces.