On Some New Modular Sequence Spaces - Bektas, Cigdem A.; Atici, Gulcan (Soc Paranaense Matematica, 2013)
Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space l(M) which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. An important subspace of l(M), which is an AK-space, is the space h (M). We define the sequence spaces l(lambda)(M)(Delta(m)) and l(N)(m)(Delta(m)), where M = (M-k) and N = (N-k) are sequences of Orlicz functions such that M-k and N-k be mutually complementary for each k. We also examine some topological properties of these spaces. We give the alpha- beta- and gamma-duals of the sequence space h (M) and alpha-duals of the squence spaces l(M, lambda) and l(N, lambda).
Keywords: Difference sequence spaces; Orlicz function; alpha-; beta- and gamma-duals