Abstract
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.
Original language | English |
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Pages (from-to) | 547-558 |
Number of pages | 12 |
Journal | Proceedings of the American Mathematical Society |
Volume | 142 |
Issue number | 2 |
DOIs | |
State | Published - 2014 |
Keywords
- Banach-saks properties
- Musielak-orlicz space
- Nakano space
- Schur property
- Variable exponent space
- Weighted orlicz space