Spaces of nonpositive curvature arising from a finite algebra (Q973991)

The authors give a family of examples that can be regarded as spaces of nonpositive curvature which are not complete metric spaces. These examples consist of endowing the cone of positive invertible operators of a finite von Neumann algebra with the rectifiable distances induced by the \(p\)-norms. In spite of the noncompleteness of these manifolds, their geometry can be studied from the view point of metric geometry.