Hostname: page-component-7c8c6479df-94d59 Total loading time: 0 Render date: 2024-03-19T05:47:10.914Z Has data issue: false hasContentIssue false

Measurable Hilbert sheaves

Published online by Cambridge University Press:  09 April 2009

Michael A. Wendt
Affiliation:
Department of Mathematics, Statistics and Computer Science Dalhousie UniversityHalifax NS B3H 4H6, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
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), 357.Google Scholar
[4]Paré, R., Schumacher, D., Abstract families and the adjoint functor theorem, in: Lecture Notes in Math. 661 (Springer, New York, 1978), 1125.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), 623659.Google Scholar
[7]Wendt, M., ‘The category of disintegrations,’ Cahiers Topologie Géom. Diffèrentielle Catégoriques 35 (1994), 291308.Google Scholar