The weak Banach-Saks property on Lp(μ, E)

Abstract

A Banach space E is said to have the Banach-Saks property (BS) if every bounded sequence (xn) in E has a subsequence (x′n) with norm convergent Cesaro means; that is, there is x in E such thatIf this occurs for every weakly convergent sequence in E it is said that E has the Weak Banach-Saks property (WBS) (also called Banach-Saks-Rosenthal property).