Banach—Saks Property and Property (β) in Cesàro Sequence Spaces

Abstract

A new constant C(X) for any Banach space X is introduced. It is proved that C(X) < 2 implies the weak Banach—Saks property for the space X. In particular, C(ces p ) is found for Cesaro sequence space ces p (1 < p < ∞). Moreover, it is shown that the space ces p (1 < p < ∞) has property (β).