Duality and stable compactness in Orlicz-type modules

Orlicz-type modules are module analogues of classical Orlicz spaces. We study duality and stable compactness in Orlicz-type modules. We characterize the conditional Köthe dual of an Orlicz-type module as the space of all σ -order continuous module homomorphisms. We find an order continuity criterion...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2024, Vol.118 (1), Article 18
Main Authors: Orihuela, José, Zapata, José M.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Homomorphisms
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Modules
Original Paper
Theoretical
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Summary:Orlicz-type modules are module analogues of classical Orlicz spaces. We study duality and stable compactness in Orlicz-type modules. We characterize the conditional Köthe dual of an Orlicz-type module as the space of all σ -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.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-023-01516-5