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A Lebesgue Decomposition Theorem for C* Algebras

Published online by Cambridge University Press:  20 November 2018

Michael Henle
Michael Henle*
Affiliation:
Oberun College, Oberlin, Ohio
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This paper, by generalizing von Neumann's proof of the Radon-Nikodym and Lebesgue decomposition theorems [3], obtains analogous results for positive linear functional on a C* algebra. The concept of "absolute continuity" used and the Radon-Nikodym portion of the resulting theorem are due to Dye [2].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 1 , March 1972 , pp. 87 - 91
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Dixmier, J., Les C*-Algèbres et leurs représentations, Gauthier-Villars, Paris, 1964.Google Scholar
2. Dye, H., "The Radon-Nikodym theorem for finite rings of operators", Trans. Amer. Math. Soc. 72 (1952), 243-280.Google Scholar
3. Riesz, F. and Sz.-Nagy, B., Functional analysis, Ungar, New York (1955), 137-140.Google Scholar