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Every (\(\beta\) )-space has the Banach-Saks property. (English) Zbl 0696.46016

The condition (\(\beta)\), introduced by S. Rolewicz [Stud. Math. 85, 27-35 (1987; Zbl 0642.46011)] describes a certain convexity property of the underlying norm of a Banach space (similar to uniform convexity, near uniform convexity, etc.). Under equivalent renorming, every (\(\beta)\)- space has the Banach-Saks property. Relations with other notions of convexity are also discussed.
Reviewer: J.Szulga

MSC:

46B20 Geometry and structure of normed linear spaces

Citations:

Zbl 0642.46011
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