SPM: www.spm.uem.br/bspm doi:10.5269/bspm.v31i2.15316 On Some New Modular Sequence Spaces

abstract: Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space ℓM 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 ℓM λ (∆m) and ℓλ 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 ℓ (M, λ) and ℓ (N, λ). Key Words:Difference sequence spaces, Orlicz function, α−, β − and γ