arXiv subjects
Publications and source records attributed to Gabriel Larotonda.
The Hilbert manifold $Σ$ consisting of positive invertible (unitized) Hilbert-Schmidt operators has a rich structure and geometry. The geometry of unitary orbits $Ω\subset Σ$ is studied from the topological and metric viewpoints: we seek for conditions that ensure the existence of a smooth local structure for the set $Ω$, and we study the convexity of this set for the geodesic structures that arise when we give $Σ$ two Riemannian metrics.
In this article we follow the main idea of A. Connes for the construction of a metric in the state space of a C*-algebra. We focus in the reduced algebra of a discrete group $Γ$, and prove some equivalences and relations between two central objects of this category: the word-length growth (connected with the degree of the extension of $Γ$ when the group is an extension of Z by a finite group), and the topological equivalence between the w*-topology and the one introduced with this metric in the state space of $C_r*(Γ)$.