Projective space of a C*-module

1999/11/20 by E. Andruchow, Andruchow, E., G. Corach +3
Mathematics · #46L05 #58B20 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05 #msc:58B20

paper · pdf · doi:10.48550/arxiv.math/9911155

22 pages, AMSTeX

arxiv created 1999/11/20 · arxiv updated 2009/11/30

Abstract

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 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.

Related

• The C*-algebra of a Hilbert Bimodule
• Projective representations of groups using Hilbert right C*-modules
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