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

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

2000-02-08

arxiv.org/abs/math/0002055v1

Mathematics

Functional Analysis

A 10 pages long AMSTeX file

Scientific paper

Given 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 M

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