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arXiv · 1702.05050

On certain geometric properties in Banach spaces of vector-valued functions

Jan-David Hardtke
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Abstract

We consider a certain type of geometric properties of Banach spaces, which includes for instance octahedrality, almost squareness, lushness and the Daugavet property. For this type of properties, we obtain a general reduction theorem, which, roughly speaking, states the following: if the property in question is stable under certain finite absolute sums (for example finite $\ell^p$-sums), then it is also stable under the formation of corresponding K\"othe-Bochner spaces (for example $L^p$-Bochner spaces). From this general theorem, we obtain as corollaries a number of new results as well as some alternative proofs of already known results concerning octahedral and almost square spaces and their relatives, diameter-two-properties, lush spaces and other classes.

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Jan-David Hardtke. 2017-02-16. On certain geometric properties in Banach spaces of vector-valued functions. https://arxiv.org/abs/1702.05050

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