Non-injectivity of Bures--Wasserstein barycentres in infinite dimensions

We construct a counterexample to the injectivity conjecture of Masarotto et al (2018). Namely, we construct a class of examples of injective covariance operators on an infinite-dimensional separable Hilbert space for which the Bures--Wasserstein barycentre is highly non injective -- it has a kernel...

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Bibliographic Details
Published inarXiv.org
Main Author Zemel, Yoav
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.11.2023
Subjects
Hilbert space
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Summary:We construct a counterexample to the injectivity conjecture of Masarotto et al (2018). Namely, we construct a class of examples of injective covariance operators on an infinite-dimensional separable Hilbert space for which the Bures--Wasserstein barycentre is highly non injective -- it has a kernel of infinite dimension.
ISSN:2331-8422