Wishart--Pickrell distributions and closures of group actions

DOI10.1007/S10958-017-3417-1arXiv1602.03492MaRDI QIDQ6270349

Publication date: 10 February 2016

Abstract: Consider probabilistic distributions on the space of infinite Hermitian matrices $Herm(infty)$ invariant with respect to the unitary group $U(infty)$. We describe the closure of $U(infty)$ in the space of spreading maps (polymorphisms) of $Herm(infty)$, this closure is a semigroup isomorphic to the semigroup of all contractive operators.

Mathematics Subject Classification ID

Operator theory (47-XX) Functional analysis (46-XX)

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