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Non-injectivity of Bures--Wasserstein barycentres in infinite dimensions
Published 15 Nov 2023 in math.FA, math.ST, and stat.TH | (2311.09385v1)
Abstract: 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.
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