Projective space of a C*-module

Andruchow, E.; Corach, G.; Stojanoff, D.

Projective space of a C*-module

Authors

Andruchow, E.

Corach, G.

Stojanoff, D.

Description

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) \to P(X), where S_p(X)={x\in X: <x,x>=p}, for p in 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 adjointable operators of X. The homotopy theory of these spaces is examined.
22 pages, AMSTeX