Characterization of Hilbertizable spaces via convex functions
Functional Analysis
2025-06-11 v1 Optimization and Control
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 then the underlying space is also isomorphic to a Hilbert space.
Cite
@article{arxiv.2506.04686,
title = {Characterization of Hilbertizable spaces via convex functions},
author = {Nicolas Borchard and Gerd Wachsmuth},
journal= {arXiv preprint arXiv:2506.04686},
year = {2025}
}
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8 pages