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arXiv · 2408.14093

Products of hyperbolic spaces

Pedro Pinto·Andrei Sipos
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Abstract

The class of uniformly smooth hyperbolic spaces was recently introduced by the first author as a common generalization of both CAT(0) spaces and uniformly smooth Banach spaces, in a way that Reich's theorem on resolvent convergence could still be proven. We define products of such spaces, showing that they are reasonably well-behaved. In this manner, we provide the first example of a space for which Reich's theorem holds and which is neither a CAT(0) space, nor a convex subset of a normed space.

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Pedro Pinto, Andrei Sipos. 2024-08-26. Products of hyperbolic spaces. https://arxiv.org/abs/2408.14093

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