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Affiliation(s)

1. Department of Mathematics, College of Sciences and Arts, University King Khalid university, Almajardah Kingdom of Saudi Arabia Asir-Abha P. O. Box: 960-Postal Code:61421
2. Mathematics Department, Faculty of Education, Nile Valley University Atbara –Sudan-Postal: Khartoum PO Box 1843

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

KEYWORDS

Banach–Saks property, property (β), Cesàro sequence space.

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