The manifold of finite rank projections in the algebra L(H) of bounded linear operators
| dc.creator | Isidro, J. M. | |
| dc.creator | Mackey, M. | |
| dc.date | 2001-10-11 | |
| dc.date.accessioned | 2026-07-07T04:43:46Z | |
| dc.date.available | 2026-07-07T04:43:46Z | |
| dc.description | Given a complex Hilbert space H, we study the differential geometry of the manifold M of all projections in V:=L(H). Using the algebraic structure of V, a torsionfree affine connection $\nabla$ (that is invariant under the group of automorphisms of V) is defined on every connected component of M, which in this way becomes a symmetric holomorphic manifold that consists of projections of the same rank r, (0< r < \infty). We prove that M admits a Riemann structure if and only if M consists of projections that have the same finite rank r or the same finite corank, and in that case $\nabla$ is the Levi-Civita and the Kähler connection of M. Moreover, M turns out to be a totally geodesic Riemann manifold whose geodesics and Riemann distance are computed. Keywords: JBW-algebras, Grassmann manifolds, Riemann manifolds. AMS 2000 Subject Classification: 48G20, 72H51. | |
| dc.description | 17 pages, Latex 2e, to appear in Expositiones Mathematicae | |
| dc.identifier | https://arxiv.org/abs/math/0110115 | |
| dc.identifier | http://arxiv.org/abs/math/0110115 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62368 | |
| dc.subject | Functional Analysis | |
| dc.subject | Differential Geometry | |
| dc.subject | 48G20, 72H51 | |
| dc.title | The manifold of finite rank projections in the algebra L(H) of bounded linear operators | |
| dc.type | text |