PROJECTIVE SPACE OF A C*-MODULE

ESTEBAN ANDRUCHOW, GUSTAVO CORACH, DEMETRIO STOJANOFF
2001 Infinite Dimensional Analysis Quantum Probability and Related Topics  
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
more » ... algebra L A (X) of adjointable operators of X. The homotopy theory of these spaces is examined.
doi:10.1142/s0219025701000516 fatcat:bm53xnarszetnk4pnqxpzuux7i