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LEBESGUE DECOMPOSITION FOR REPRESENTABLE FUNCTIONALS ON *-ALGEBRAS

Part of: Selfadjoint operator algebras General theory of linear operators Topological (rings and) algebras with an involution

Published online by Cambridge University Press:  21 July 2015

ZSIGMOND TARCSAY
ZSIGMOND TARCSAY*
Affiliation:
Department of Applied Analysis, Eötvös L. University, Pázmány Péter sétány 1/c., Budapest H-1117, Hungary e-mail: [email protected]
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Abstract

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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.

MSC classification

Primary: 46L45: Decomposition theory for $C^*$-algebras
Secondary: 47A67: Representation theory 46K10: Representations of topological algebras with involution
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 2 , May 2016 , pp. 491 - 501
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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