Go to  Advanced Search

Please note that cIRcle is currently being upgraded to DSpace v5.1. The upgrade means that the cIRcle service will *not* be accepting new submissions from 5:00 PM on September 1, 2015 until 5:00 PM on September 4, 2015. All cIRcle material will still be accessible during this period. Apologies for any inconvenience.

Abelian von Neumann algebras

Show full item record

Files in this item

Files Size Format Description   View
UBC_1966_A8 K47.pdf 4.233Mb Adobe Portable Document Format   View/Open
Title: Abelian von Neumann algebras
Author: Kerr, Charles R.
Degree Master of Arts - MA
Program Mathematics
Copyright Date: 1966
Subject Keywords Rings (Algebra); Abelian groups
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.
URI: http://hdl.handle.net/2429/36976
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]
Scholarly Level: Graduate

This item appears in the following Collection(s)

Show full item record

All items in cIRcle are protected by copyright, with all rights reserved.

UBC Library
1961 East Mall
Vancouver, B.C.
Canada V6T 1Z1
Tel: 604-822-6375
Fax: 604-822-3893