Symmetries of Gaussian measures and operator colligations

Abstract

Consider an infinite-dimensional linear space equipped with a Gaussian measure and the group $GL(\infty )$ of linear transformations that send the measure to equivalent one. Limit points of $GL(\infty )$ can be regarded as 'spreading' maps (polymorphisms). We show that the closure of $GL(\infty )$ in the semigroup of polymorphisms contains a certain semigroup of operator colligations and write explicit formulas for action of operator colligations by polymorphisms of the space with Gaussian measure.

21pp

References in corpus (1)

• On the boundary of the group of transformations leaving a measure quasi-invariant

Cited by in corpus (4)

• Symmetric groups and checker triangulated surfaces
• Wishart--Pickrell distributions and closures of group actions
• On the boundary of the group of transformations leaving a measure quasi-invariant
• Several remarks on groups of automorphisms of free groups