Projective space of a C*-module

E. Andruchow; G. Corach; D. Stojanoff

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arXiv · math/9911155

Projective space of a C*-module

E. Andruchow·G. Corach·D. Stojanoff

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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) \to P(X), where S_p(X)={x\in 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.

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BibTeX RIS

E. Andruchow, G. Corach, D. Stojanoff. 1999-11-20. Projective space of a C*-module. https://arxiv.org/abs/math/9911155

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