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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.

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

Citations:

Zbl 0652.46010
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