On some new modular sequence spaces

Abstract

Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space â„“M which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. An important subspace of â„“ (M), which is an AK-space, is the space h (M) . We define the sequence spaces â„“M (m) and â„“ N(m), where M = (Mk) and N = (Nk) are sequences of Orlicz functions such that Mk and Nk be mutually  complementary for each k. We also examine some topological properties of these spaces. We give the α−, β− and γ− duals of the sequence space h (M) and α− duals of the squence spaces â„“ (M, λ) and â„“ (N, λ).