On some new modular sequence spaces

Abstract

Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space ?M which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. An important subspace of ?(M), which is an AK-space, is the space h(M). We define the sequence spaces ?M? (?m) and ?N?(?m), where M = (M k) 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 ?-, ?- and ?-duals of the sequence space h (M) and ?- duals of the squence spaces ?(M, ?) and ?(N, ?). © SPM.