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

José M. Isidro
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Abstract

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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José M. Isidro. 2000-02-08. The manifold of finite rank projections in the space L(H). https://arxiv.org/abs/math/0002055

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