Banach–Saks Property and PropertyβInCesàro Sequence Spaces

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(cesp)is found for Cesàro sequence space cesp(1<p<∞).Moreover,it is shown that the space cesp(1<p<∞)has property(β).