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Abelian von Neumann algebras

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dc.contributor.author Kerr, Charles R.
dc.date.accessioned 2011-08-30T16:28:56Z
dc.date.available 2011-08-30T16:28:56Z
dc.date.copyright 1966
dc.date.issued 2011-08-30
dc.identifier.uri http://hdl.handle.net/2429/36976
dc.description.abstract This thesis carries out some of classical integration theory in the context of an operator algebra. The starting point is measure on the projections of an abelian von Neumann algebra. This yields an integral on the self-adjoint operators whose spectral projections lie in the algebra. For this integral a Radon-Nikodym theorem, as well as the usual convergence theorems is proved. The methods and results of this thesis generalize, to non-commutative von Neumann Algebras [2, 3, 5]. (1) J. Dixmier Les Algèbres d'Opérateurs dans l'Espace Hilbertien. Paris, 1957. (2) H.A. Dye The Radon-Nikodym theorem for finite rings of operators, Trans. Amer. Math. Soc, 72, 1952, 243-230. (3) F.J. Murray and J. von Neumann, On Rings of Operators, Ann. Math. 37, 1936, 116-229. (4) F. RIesz and B. v. Sz.-Nagy, Functional Analysis, New York, 1955. (5) I.E. Segal A non-commutative extension of abstract integration, Ann. of Math. (2) 57, 1953, 401-457. en_US
dc.language.iso eng en_US
dc.publisher University of British Columbia en
dc.relation.ispartofseries UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/] en
dc.subject Rings (Algebra) en_US
dc.subject Abelian groups en_US
dc.title Abelian von Neumann algebras en_US
dc.type Electronic Thesis or Dissertation en
dc.degree.name Master of Arts - MA en_US
dc.degree.discipline Mathematics en_US
dc.degree.grantor University of British Columbia en
dc.degree.campus UBCV en_US
dc.description.scholarlevel Graduate en


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