BANACH-SAKS PROPERTIES OF MUSIELAK-ORLICZ AND NAKANO SEQUENCE SPACES

Abstract

In this paper Banach-Saks properties of Musielak-Orlicz sequence space l(phi) F are studied. It is shown that l(phi) F has the weak Banach-Saks property if and only if it is separable. Moreover it is proved that in l(phi) F both Banach-Saks type p-properties, (BSp) and (S-p), are equivalent and that the Schur property and (BS infinity) 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 l(phi)(w), in terms of the sequence (p(n)), and the Orlicz function phi and the weight sequence w, respectively.