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PROJECTIVE SPACE OF A C*-MODULE

2001
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Infinite Dimensional Analysis Quantum Probability and Related Topics
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Let X be a right Hilbert C * -module over A. We study the geometry and the topology of the projective space P(X) of X, consisting of the orthocomplemented submodules of X which are generated by a single element. We also study the geometry of the p-sphere S p (X) and the natural fibration S p (X) → P(X), where S p (X) = {x ∈ X : x, x = p}, for p ∈ A a projection. The projective space and the p-sphere are shown to be homogeneous differentiable spaces of the unitary group of the algebra L A (X) of

doi:10.1142/s0219025701000516
fatcat:bm53xnarszetnk4pnqxpzuux7i