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

Anna Kamińska, Han Ju Lee

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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 languageEnglish
Pages (from-to)547-558
Number of pages12
JournalProceedings of the American Mathematical Society
Volume142
Issue number2
DOIs
StatePublished - 2014

Keywords

  • Banach-saks properties
  • Musielak-orlicz space
  • Nakano space
  • Schur property
  • Variable exponent space
  • Weighted orlicz space

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