Metric Geometry in Homogeneous Spaces of the Unitary Group of a C*-Algebra. Part II. Geodesics Joining Fixed Endpoints

This article focuses on the study of the metric geometry of homogeneous spaces (the unitary group of a C*-algebra modulo the unitary group of a C*-subalgebra ) where the invariant Finsler metric in is induced by the quotient norm of Under the assumption that is of compact type, i.e. when the unitary group is relatively compact in the strong operator topology, this work presents local and global versions of Hopf-Rinow-like theorems: given points there exists a minimal uniparametric group curve joining ρ₀ and ρ₁.