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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Lebesgue decomposition of positive linear functionals


Author: Zsolt Szũcs
Journal: Proc. Amer. Math. Soc. 141 (2013), 619-623
MSC (2010): Primary 46L51; Secondary 46C50, 46L30
Published electronically: June 26, 2012
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Abstract: In this paper we will prove that the Lebesgue decomposition of positive linear functionals on Banach $ ^*$-algebras corresponds with the Lebesgue decomposition of the nonnegative forms derived from the functionals.


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Additional Information

Zsolt Szũcs
Affiliation: Department of Applied Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117 Budapest, Hungary
Email: szzsolti@cs.elte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11354-1
PII: S 0002-9939(2012)11354-1
Keywords: Nonnegative forms, positive functionals, Lebesgue type decomposition, singularity
Received by editor(s): September 17, 2010
Received by editor(s) in revised form: July 8, 2011
Published electronically: June 26, 2012
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.