Work

Some results on the Orlicz space generated from a random normed module

Year: 2015

Type: preprint

Abstract: Noting the important role the abstract $L^p$ space has played in the development of random normed modules, in this paper we introduce and study the Orlicz space generated from a random normed module. First, we give a basic dual space representation theorem which identify the dual of the Orlicz heart of a random normed module with the Orlicz space generated from the random conjugate space. Then, we establish the respective equivalence relations of the strict convexity and uniform convexity of this abstract Orlicz space to the random strict convexity and random uniform convexity of the underlying random normed module. These results demonstrate that it is possible to use the Orlicz space theory in the further development of random nomed modules.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1511.00940

Authors: Wu, Mingzhi, Long, Long, Zeng, Xiaolin

Institutions: China University of Geosciences, Central South University, Chongqing Technology and Business University

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Chongqing Technology and Business University, China University of Geosciences, Fundamental Research Funds for the Central Universities

Awards: G2422330955, G732175170, G7781476517, G8463821988

OpenAlex ID: W2907787093

Cites: 22

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Related to: 10