Banach-saks properties of musielak-orlicz and nakano sequence spaces


In this paper Banach-Saks properties of Musielak-Orlicz sequence space ℓΦ are studied. It is shown that ℓΦ has the weak Banach-Saks property if and only if it is separable. Moreover it is proved that in ℓΦ both Banach-Saks type p-properties, (BSp) and (Sp), are equivalent and that the Schur property and (BSqg) also coincide in these spaces. As applications, we give characterizations of the weak Banach-Saks property and the (BSp) property in the Nakano sequence space ℓ(pn) and weighted Orlicz sequence space ℓφ(w), in terms of the sequence (pn), and the Orlicz function φ and the weight sequence w, respectively. © 2013 American Mathematical Society.

Publication Title

Proceedings of the American Mathematical Society