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arXiv · 2412.00891

Tingley's problem for Schreier spaces and their $p$-convexifications

Micheline Fakhoury
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Abstract

We describe the surjective isometries of the unit sphere of real Schreier spaces of all orders and their $p$-convexifications, for $1 < p < \infty$. This description allows us to provide for those spaces a positive answer to a special case of Tingley's problem, which asks whether every surjective isometry of the unit sphere of a real Banach space can be extended to a linear isometry of the entire space.

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Micheline Fakhoury. 2024-12-01. Tingley's problem for Schreier spaces and their $p$-convexifications. https://arxiv.org/abs/2412.00891

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