On certain Opial-type results in Ces\`aro spaces of vector-valued functions

Abstract

Given a Banach space $X$, we consider Ces\`aro spaces $\text{Ces}_p(X)$ of $X$-valued functions over the interval $[0,1]$, where $1\leq p<\infty$. 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 Ces\`aro spaces of vector-valued sequences.