On Subsequential Averages of Sequences in Banach Spaces

Abstract

For a sequence in a Banach space $\mathcal{X}$, it is known that the set of subsequential limits of the sequence forms a closed subset of $\mathcal{X}$. Similarly, if the sequence is convergent, then the sequence of its Cesàro averages also converge to the same value. In this article, we study the properties of the set of Cesàro limits of subsequences of a given sequence in a Banach space using techniques from ergodic theory.