Abstract
In a recent paper of Kasparov [K] the theory of Hilbert modules over noncommutative C* -algebras is used to establish a general theory of extensions of C*-algebras that extends results of Brown, Douglas, and Fillmore [BDF], Fillmore [F], and Pimsner, Popa, and Voiculescu [PPV]. Since the category of Hilbert C (X) -modules is equivalent to the category of Hilbert bundles over X [DD;DG], many questions of topological interest can be recast in terms of Hilbert C(X)-modules which then give rise to questions about general Hilbert modules. In particular, Kasparov’s stability theorem [K] (which plays an essential part in the proof that inverses exist in the general theory of EXT) is the noncommutative extension of a triviality theorem of Dixmier and Douady [DD, Th.4] (which itself provides the existence of classifying maps for arbitrary separable Hilbert bundles over paracompact spaces).
Partially supported by the National Science Foundation.
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© 1981 Springer Basel AG
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Dupré, M.J., Fillmore, P.A. (1981). Triviality Theorems for Hilbert Modules. In: Apostol, C., Douglas, R.G., Nagy, B.S., Voiculescu, D., Arsene, G. (eds) Topics in Modern Operator Theory. Operator Theory: Advances and Applications, vol 2. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5456-6_6
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DOI: https://doi.org/10.1007/978-3-0348-5456-6_6
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