Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-2012-11354-1
Published electronically: June 26, 2012
MathSciNet review: 2996966
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. J. Dixmier, $ C^*$-algebras. Translated from the French by Francis Jellett. North-Holland Mathematical Library, Vol. 15, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. MR 0458185 (56:16388)
  • 2. S. P. Gudder, A Radon-Nikodým theorem for $ ^*$-algebras, Pacific J. Math., Vol. 80, No. 1 (1979), 141-149. MR 534703 (80g:46057)
  • 3. S. Hassi, Z. Sebestyén, H. de Snoo, Lebesgue type decompositions for nonnegative forms, Journal of Functional Analysis, Vol. 257, Issue 12 (2009), 3858-3894. MR 2557727 (2010k:47042)
  • 4. T. W. Palmer, Banach Algebras and the General Theory of $ ^*$-Algebras II. Cambridge University Press (2001). MR 1819503 (2002e:46002)
  • 5. G. K. Pedersen, $ C^*$-algebras and their automorphism groups. London Mathematical Society Monographs, 14, Academic Press, Inc. [Hartcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006 (81e:46037)
  • 6. S. Sakai, $ C^*$-algebras and $ W^*$-algebras. Ergebnisse der Mathematik und ihrer Grezengebeite, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701 (56:1082)
  • 7. Z. Sebestyén, On representability of linear functionals on $ ^*$-algebras, Period. Math. Hungar. 15 (1984), no. 3, 233-239. MR 756188 (86a:46068)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46L51, 46C50, 46L30

Retrieve articles in all journals with MSC (2010): 46L51, 46C50, 46L30


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: https://doi.org/10.1090/S0002-9939-2012-11354-1
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.

American Mathematical Society