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arXiv · 2311.07319

Banach-Saks Theorem for $L^1$ revisited

Guy Foghem
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Abstract

The Banach-Saks property is an important tool in analysis with applications ranging from partial differential equations (PDEs) to calculus of variations and probability theory. We survey the Banach-Saks property for $L^p$-spaces, with a particular emphasis on the case where $p=1$. In other words, we revisit the celebrated result by W. Szlenk (1965) in a more general context, demonstrating that $L^1$-spaces possess the weak Banach-Saks property.

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Guy Foghem. 2023-11-13. Banach-Saks Theorem for $L^1$ revisited. https://arxiv.org/abs/2311.07319

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