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On isometries of Wasserstein spaces (Research on preserver problems on Banach algebras and related topics)

GEHÉR György Pál TITKOS, Tamás VIROSZTEK, Dániel 京都大学

2023.07

概要

It is known that if p ≥ 1, then the isometry group of the metric space (X, ϱ) embeds into the isometry group of the Wasserstein space Wp(X, ϱ). Those isometries that belong to the image of this embedding are called trivial. In many concrete cases, all isometries are trivial, however, this is not always the case. The aim of this survey paper is to provide a structured overview of recent results concerning trivial and different types of nontrivial isometries.

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