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A Hilbert bundle characterization of Hilbert \(C^*\)-modules. (English) Zbl 1154.46033

Summary: 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.

MSC:

46L08 \(C^*\)-modules
46M15 Categories, functors in functional analysis
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