WORTH property, Garc\'{i}a-Falset coefficient and Opial property of infinite sums

Abstract

We prove some results concerning the WORTH property and the Garc\'{i}a-Falset coefficient of absolute sums of infinitely many Banach spaces. The Opial property/uniform Opial property of infinite $\ell^p$-sums is also studied and some properties analogous to the Opial property/uniform Opial property for Lebesgue-Bochner spaces $L^p(\mu,X)$ are discussed.