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Measurable Hilbert sheaves

Part of: Categories with structure Special categories Special classes of linear operators Classical measure theory

Published online by Cambridge University Press:  09 April 2009

Michael A. Wendt
Michael A. Wendt
Affiliation:
Department of Mathematics, Statistics and Computer Science Dalhousie UniversityHalifax NS B3H 4H6, Canada
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Abstract

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We describe measurable Hilbert sheaves as Hilbert space objects in a sheaf category constructed from a measure space. These are quite useful for the interpretation of the direct integral of Hilbert spaces as an indexed functor. We set up a framework to put this and similar constructions of operator theory on an indexed categorical footing.

MSC classification

Secondary: 18B25: Topoi 18D35: Structured objects in a category (group objects, etc.) 28A50: Integration and disintegration of measures 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 2 , October 1996 , pp. 189 - 215
Copyright
Copyright © Australian Mathematical Society 1996

References

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