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arXiv · 2506.04686

Characterization of Hilbertizable spaces via convex functions

Nicolas Borchard·Gerd Wachsmuth
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Abstract

We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then the underlying space is also isomorphic to a Hilbert space.

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Nicolas Borchard, Gerd Wachsmuth. 2025-06-05. Characterization of Hilbertizable spaces via convex functions. https://arxiv.org/abs/2506.04686

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