The manifold of finite rank projections in the space L(H)

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58649Given a complex Hilbert space H and the von Neumann algebra L(H) of all bounded linear operators on H, we study the Grassmann manifold M of all projections in L(H) that have a fixed finite rank r. We take the Jordan-Banach triple theory approach which allows us to define a natural Levi-Civita connection on M. We identify the geodesics, compute the Riemann distance and prove some properties of MA 10 pages long AMSTeX fileFunctional AnalysisDifferential Geometry17C99 (Primary) 53C35 (Secondary)The manifold of finite rank projections in the space L(H)text