Banach–Saks Property and Property β InCesàro 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( ) is found for Cesàro sequence space (1 < p < ∞ ). Moreover, it is shown that the space (1 < p < ∞) has property .