Geodesic
LEBESGUE DECOMPOSITION FOR REPRESENTABLE FUNCTIONALS ON *-ALGEBRAS
Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 491-501

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DOI

We offer a Lebesgue-type decomposition of a representable functional on a *-algebra into absolutely continuous and singular parts with respect to another. Such a result was proved by Zs. Szűcs due to a general Lebesgue decomposition theorem of S. Hassi, H.S.V. de Snoo, and Z. Sebestyén concerning non-negative Hermitian forms. In this paper, we provide a self-contained proof of Szűcs' result and in addition we prove that the corresponding absolutely continuous parts are absolutely continuous with respect to each other. 
TARCSAY, ZSIGMOND. LEBESGUE DECOMPOSITION FOR REPRESENTABLE FUNCTIONALS ON *-ALGEBRAS. Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 491-501. doi: 10.1017/S0017089515000300
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     author = {TARCSAY, ZSIGMOND},
     title = {LEBESGUE {DECOMPOSITION} {FOR} {REPRESENTABLE} {FUNCTIONALS} {ON} {*-ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {491--501},
     year = {2016},
     volume = {58},
     number = {2},
     doi = {10.1017/S0017089515000300},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000300/}
}
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