Geodesic
A Lebesgue Decomposition Theorem for C * Algebras
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 87-91

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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]. 
Henle, Michael. A Lebesgue Decomposition Theorem for C * Algebras. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 87-91. doi: 10.4153/CMB-1972-016-2
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     author = {Henle, Michael},
     title = {A {Lebesgue} {Decomposition} {Theorem} for {C} * {Algebras}},
     journal = {Canadian mathematical bulletin},
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     year = {1972},
     volume = {15},
     number = {1},
     doi = {10.4153/CMB-1972-016-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-016-2/}
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