The order-type Banach-Saks properties

Tantrawan, Made and Leung, Denny H and Gao, Niushan (2023) The order-type Banach-Saks properties. Journal of Mathematical Analysis and Applications, 517 (1). ISSN 0022247X

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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.

Item Type: Article
Uncontrolled Keywords: Banach function spaces; Banach-Saks property; Order Banach-Saks property; Order convergence; Orlicz spaces; Rearrangement invariant spaces
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Mathematics and Natural Sciences > Mathematics Department
Depositing User: Ismu WIDARTO
Date Deposited: 26 Sep 2024 00:40
Last Modified: 26 Sep 2024 00:40
URI: https://ir.lib.ugm.ac.id/id/eprint/7547

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