Cui, Yunan; Hudzik, Henryk; Płuciennik, Ryszard Banach-Saks property in some Banach sequence spaces. (English) Zbl 0895.46010 Ann. Pol. Math. 65, No. 2, 193-202 (1997); errata ibid. 65, No. 3, 303 (1997). Summary: It is proved that for any Banach space \(X\) property \((\beta)\) defined by S. Rolewicz [in Stud. Math. 87, 181-191 (1987; Zbl 0652.46010)] implies that both \(X\) and \(X^*\) have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property \(({\mathbf H})\) are given. Cited in 6 Documents MSC: 46B45 Banach sequence spaces 46A45 Sequence spaces (including Köthe sequence spaces) 46E40 Spaces of vector- and operator-valued functions 46B22 Radon-Nikodým, Kreĭn-Milman and related properties 46B20 Geometry and structure of normed linear spaces Keywords:property \((\beta)\); Banach-Saks property; Musielak-Orlicz sequence spaces; near uniform convexity; uniform Kadec-Klee property; property \(({\mathbf H})\) Citations:Zbl 0652.46010 PDFBibTeX XMLCite \textit{Y. Cui} et al., Ann. Pol. Math. 65, No. 2, 193--202 (1997; Zbl 0895.46010) Full Text: DOI