Isomorphic copies of $l^\infty$ in Ces\`aro-Orlicz function spaces

TL;DR

This paper characterizes when Cesàro-Orlicz spaces contain isomorphic copies of l-infinity, describes their order continuous subspaces, and analyzes their monotonicity structure.

Contribution

It provides a complete characterization of isomorphic copies of l-infinity in Cesàro-Orlicz spaces and explores their order continuity and monotonicity properties.

Findings

Cesàro-Orlicz spaces contain isomorphic copies of l-infinity under specific conditions.

The structure of order continuous elements in Cesàro-Orlicz spaces is fully described.

The monotonicity properties of Cesàro-Orlicz spaces are analyzed and characterized.

Abstract

We characterize Ces\`aro-Orlicz function spaces $Ces_\varphi$ containing isomorphic copy of $l^\infty$. We also describe the subspaces $(Ces_\varphi)_a$ of all order continuous elements of $Ces_\varphi$. Finally, we study the monotonicity structure of the spaces $Ces_\varphi$ and $(Ces_\varphi)_a$.