Duality and stable compactness in Orlicz-type modules

TL;DR

This paper investigates duality and stable compactness in Orlicz-type modules, providing characterizations of dual spaces and criteria for compactness, with applications to conditional risk measures.

Contribution

It introduces a characterization of the dual space and an order continuity criterion for stable compactness in Orlicz-type modules, advancing the theoretical understanding of these structures.

Findings

Characterization of the conditional Köthe dual as $\sigma$-order continuous module homomorphisms

Order continuity criterion for stable compactness in Orlicz-type modules

Robust representation of conditional risk measures on Orlicz spaces

Abstract

Orlicz-type modules are module analogues of classical Orlicz spaces. We study duality and stable compactness in Orlicz-type modules. We characterize the conditional K\"{o}the dual of an Orlicz-type module as the space of all $\sigma$-order continuous module homomorphisms. We find an order continuity criterion for stable compactness in Orlicz-type modules. As an application, we obtain a robust representation result for conditional risk measures on Orlicz spaces.