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Measurable Hilbert sheaves

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

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

[1]Dixmier, J., Les algèbres d'opérateurs dans l'espace Hilbertien (Gauthier-Villars, Paris, 1969).Google Scholar
[2]Howlett, C. R., Universal algebra in topoi (Ph. D. Thesis, McMaster, 1973).Google Scholar
[3]Mulvey, C., Intuitionistic algebra and representations of rings, Mem. Amer. Math. Soc. 148 (1974), 3–57.Google Scholar
[4]Paré, R., Schumacher, D., Abstract families and the adjoint functor theorem, in: Lecture Notes in Math. 661 (Springer, New York, 1978), 1–125.Google Scholar
[5]Johnstone, P. T., Topos theory, London Math. Soc. Monographs 10 (Academic Press, London, 1977).Google Scholar
[6]Rousseau, C., ‘Topos theory and complex analysis’, in: Lecture Notes in Math. 753 (Springer, New York, 1979), 623–659.Google Scholar
[7]Wendt, M., ‘The category of disintegrations,’ Cahiers Topologie Géom. Diffèrentielle Catégoriques 35 (1994), 291–308.Google Scholar