A dual representation theorem on the conditional Orlicz space generated from a random normed module

2025/01/01 by Zhang, Xia, Qian, Ke, Liu, Ming
#46B20 #46E30 #46H25 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2501.00853

Abstract

In this paper, we first introduce the notion of a random Orlicz function, and further present the conditional Orlicz space generated from a random normed module. Second, we prove the denseness of the Orlicz heart of a random normed module E in E with respect to the (ε, λ)-topology. Finally, based on the above work, we establish a dual representation theorem on the conditional Orlicz space generated from a random normed module, which extends and improves some known results.

Related

• Some results on the Orlicz space generated from a random normed module
• On the Random Conjugate Spaces of a Random Locally Convex Module
• The Goldstine-Weston theorem in random normed modules
• The relations among the notions of various kinds of stability and their applications
• Closed subspaces and some basic topological properties of noncommutative Orlicz spaces