Lebesgue decomposition for representable functionals on ^*-algebras

2014/06/24 by Tarcsay, Zsigmond
#47A67 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46L45 #Secondary 46K10

paper · doi:10.48550/arxiv.1406.6156

Abstract

We present a Lebesgue-type decomposition for a representable functional on a ^*-algebra into absolutely continuous and singular parts with respect to an other. This generalizes the corresponding results of S. P. Gudder for unital Banach ^*-algebras. We also prove that the corresponding absolutely continuous parts are absolutely continuous with respect to each other.

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