We study global dynamical properties of the isometry group of the Borel randomization of a separable complete structure. In particular, we show that if properties such as the Rohklin property, topometric generics, extreme ...

In this work we investigate families of compact Lorentzian manifolds in dimension four. We show that every lightlike geodesic on such spaces is periodic, while there are closed and non-closed spacelike and timelike geodesics. ...

Let a be a C^*-algebra. In this paper the sets I of partial isometries and I_Δ ⊂ I of partial unitaries (i.e., partial isometries which commute with their adjoints) are studied from a differential geometric point of view. ...

This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples showing substantial differences with the ...

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several ...

A known general program, designed to endow the quotient space UA/UB of the unitary groups UA, UB of the C∗ algebras B⊂A with an invariant Finsler metric, is applied to obtain a metric for the space I(H) of partial isometries ...

A simple Almost-Riemannian Structure on a Lie group G is defined by a linear vector field (that is an infinitesimal automorphism) and dim(G) - 1 left-invariant ones. It is first proven that two different ARSs are isometric ...

We consider norms on a complex separable Hilbert space such that ⟨aξ,ξ⟩≤‖ξ‖2≤⟨bξ,ξ⟩ for positive invertible operators a and b that differ by an operator in the Schatten class. We prove that these norms have unitarizable ...