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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A Hilbert bundle characterization of Hilbert C*-modules


Authors: George A. Elliott and Katsunori Kawamura
Journal: Trans. Amer. Math. Soc. 360 (2008), 4841-4862
MSC (2000): Primary 46L05
DOI: https://doi.org/10.1090/S0002-9947-08-04600-X
Published electronically: April 24, 2008
MathSciNet review: 2403706
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Abstract: The category of Hilbert C*-modules over a given C*-algebra is shown to be equivalent to a certain simply described category of Hilbert bundles (i.e., continuous fields of Hilbert spaces) over the space of pure states of the C*-algebra with the zero functional adjoined.


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Additional Information

George A. Elliott
Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4
Email: elliott@math.toronto.edu

Katsunori Kawamura
Affiliation: Department of Mathematics, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
Email: kawamura@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-08-04600-X
Received by editor(s): August 28, 2006
Published electronically: April 24, 2008
Additional Notes: The work of the first author was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
Article copyright: © Copyright 2008 American Mathematical Society