Natural variational problems in the Grassmann manifold of a \(C^*\)-algebra with trace
The authors introduce a new Finsler structure of the Grassmann manifold of a \(C^*\)-algebra with trace and they study its convex properties. The main results of the paper describe the geodesic structure of this manifold. Among other things the authors prove that the extremals are the usual geodesics. A minimality theorem for some geodesics is also established. In an appendix, an interesting discussion concerning the equivalence of two approaches for the definition of length of an arc is provided.
scientific article; zbMATH DE number 1525154
scientific article