Consider probability distributions on the space of infinite Hermitian matrices Herm(∞) invariant with respect to the unitary group U(∞). We describe the closure of U(∞) in the semigroup of spreading maps (polymorphisms) of Herm(∞); this closure is a semigroup isomorphic to the semigroup of all contractive operators.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 448, 2016, pp. 236–245.
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Neretin, Y.A. The Whishart–Pickrell Distributions and Closures of Group Actions. J Math Sci 224, 328–334 (2017). https://doi.org/10.1007/s10958-017-3417-1
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DOI: https://doi.org/10.1007/s10958-017-3417-1