The order-type Banach-Saks properties

2020/10/11 by Made Tantrawan, Denny H. Leung, Tantrawan, Made +3
Decision Sciences · Economics, Econometrics and Finance · #46B42 #46E30 #Economic theories and models #FOS: Mathematics #Functional Analysis (math.FA) #Housing Market and Economics #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2010.05255

openalex publication_date 2020/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study of the Banach-Saks property in Banach spaces has a long and illustrious history. Of late, motivated by applications in financial mathematics, interest has arisen in the Banach-Saks type properties with respect to order convergence. This paper presents a study of order Banach-Saks properties in Banach function spaces, and in particular in rearrangement invariant spaces. Among the results obtained, we provide some sufficient conditions for the (weak) order Banach-Saks property. We also characterize the (weak) order Banach-Saks property in Orlicz spaces. It is also shown that the (weak) order Banach-Saks property is equivalent to its hereditary version.

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