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arXiv · 2511.19382

The metric geometry of subspaces and convex cones of the Banach space revisited

A. B. Németh
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Abstract

It is proved that the linearity of metric projections on subspaces and the convexity of the polars of the convex cones in the uniformly convex and uniformly smooth Banach space are equivalent, and both of them is equivalent with the fact that the space is an inner product space.

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A. B. Németh. 2025-11-24. The metric geometry of subspaces and convex cones of the Banach space revisited. https://arxiv.org/abs/2511.19382

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