A short proof of some recent results related to Ces{\`a}ro function spaces

TL;DR

This paper provides a concise proof of recent findings regarding the properties of Cesàro function spaces, specifically their non-duality, weak Banach-Saks property, and lack of Radon-Nikodym property.

Contribution

It offers a simplified proof of key properties of Cesàro function spaces, enhancing understanding of their structure and functional analysis characteristics.

Findings

Cesàro function spaces are not dual spaces

They possess the weak Banach-Saks property

They lack the Radon-Nikodym property

Abstract

We give a short proof of the recent results that, for every $1\leq p< \infty,$ the Ces{\`a}ro function space $Ces_p(I)$ is not a dual space, has the weak Banach-Saks property and does not have the Radon-Nikodym property.