双曲空间的乘积

arXiv - MATH - Metric Geometry Pub Date : 2024-08-26 DOI:arxiv-2408.14093

Andrei Sipos

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引用次数: 0

摘要

平托（Pinto）最近引入了均匀光滑双曲空间类，将其作为 CAT(0) 空间和均匀光滑巴纳赫空间的共同广义，从而仍然可以证明赖希的解析收敛定理。我们定义了此类空间的乘积，证明它们具有合理的良好行为。通过这种方式，我们首次举例说明了赖希定理成立的空间，它既不是 CAT(0) 空间，也不是规范空间的凸子集。

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Products of hyperbolic spaces

The class of uniformly smooth hyperbolic spaces was recently introduced by Pinto 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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arXiv - MATH - Metric Geometry

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