DUALS OF GENERALIZED ORLICZ HILBERT SEQUENCE SPACES and MATRIX TRANSFORMATIONS

Abstract

In this paper, we define the sequence spaces h_{c}(Δ_{v}^{(m)},M,u,p), h₀(Δ_{v}^{(m)},M,u,p) and h_{∞}(Δ_{v}^{(m)},M,u,p) resulting from the infinite Hilbert matrix and the Musielak-Orlicz function. We give some topological properties and inclusion relations of these newly created spaces. We also identified α-,β- and γ-duals of the spaces. Finally, we tried to characterize some matrix transformations between these spaces.