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)

 
 

 

A cross section theorem and an application to $ C\sp*$-algebras


Authors: Robert R. Kallman and R. D. Mauldin
Journal: Proc. Amer. Math. Soc. 69 (1978), 57-61
MSC: Primary 28A05; Secondary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1978-0463390-8
MathSciNet review: 0463390
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this note is to prove a cross section theorem for certain equivalence relations on Borel subsets of a Polish space. This theorem is then applied to show that cross sections always exist on countably separated Borel subsets of the dual of a separable $ {C^ \ast }$-algebra.


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

  • [1] L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), 255-354. MR 0293012 (45:2092)
  • [2] L. Auslander and C. C. Moore, Unitary representations of solvable Lie groups, Mem Amer. Math. Soc., no. 62 (1966). MR 0207910 (34:7723)
  • [3] N. Bourbaki, General topology. II, Hermann, Paris, 1966.
  • [4] J. Dixmier, Dual et quasi-dual d'une algèbre de Banach involutive, Trans. Amer. Math. Soc. 104 (1962), 278-283. MR 0139960 (25:3384)
  • [5] -, Les $ {C^\ast}$-algebres et leurs representations, Gauthier-Villars, Paris, 1969. MR 0246136 (39:7442)
  • [6] E. G. Effros, Transformation groups and $ {C^\ast}$-algebras, Ann. of Math. 81 (1965), 38-55. MR 0174987 (30:5175)
  • [7] -, A decomposition theory for representations of $ {C^\ast}$-algebras, Trans. Amer. Math. Soc. 107 (1963), 83-106. MR 0146682 (26:4202)
  • [8] H. Hahn, Reelle Funktionen, Akad.-Verlag, Leipzig, 1932.
  • [9] C. Kuratowski, Topology. I, Academic Press, New York, 1966. MR 0193605 (33:1823)
  • [10] W. Sierpinski, Sur deux complémentaires analytiques non separables, Fund. Math. 17 (1931), 296-297.
  • [11] A. D. Taimanov, On open images of Borel sets, Mat. Sb. 37 (1955), 293-300. MR 0075581 (17:772c)
  • [12] G. W. Mackey, Borel structure in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 134-165. MR 0089999 (19:752b)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A05, 46L05

Retrieve articles in all journals with MSC: 28A05, 46L05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0463390-8
Keywords: Quotient Borel space, Borel cross section, $ {C^ \ast }$-algebra
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society