WORTH property, García-Falset coefficient and Opial property of infinite sums

Abstract

We prove some results concerning the WORTH property and the García-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.

arXiv comment22 pages