On certain Opial-type results in Cesàro spaces of vector-valued functions

Abstract

Given a Banach space $X$, we consider Cesàro spaces ${\text{Ces}}_p(X)$ of $X$-valued functions over the interval $[0,1]$, where $1\le p<\infty$. We prove that if $X$ has the Opial/uniform Opial property, then certain analogous properties also hold for ${\text{Ces}}_p(X)$. We also prove a result on the Opial/uniform Opial property of Cesàro spaces of vector-valued sequences.

15 pages, partial text overlap with arXiv:1403.2647