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 (m) and ℓ 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).
@article{15316,
title = {On some new modular sequence spaces},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {31},
year = {2013},
doi = {10.5269/bspm.v31i2.15316},
language = {EN},
url = {http://dml.mathdoc.fr/item/15316}
}
Bektas, Cigdem Asma; Atıci, Gülcan. On some new modular sequence spaces. Boletim da Sociedade Paranaense de Matemática, Tome 31 (2013) . doi : 10.5269/bspm.v31i2.15316. http://gdmltest.u-ga.fr/item/15316/