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arXiv · 2010.05255

The order-type Banach-Saks properties

Made Tantrawan·Denny H. Leung·Niushan Gao
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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.

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Made Tantrawan, Denny H. Leung, Niushan Gao. 2020-10-11. The order-type Banach-Saks properties. https://arxiv.org/abs/2010.05255

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