Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A generalized Kakutani-Kodaira theorem

Author: Zhiguo Hu
Journal: Proc. Amer. Math. Soc. 133 (2005), 3437-3440
MSC (2000): Primary 22D05
Published electronically: May 9, 2005
MathSciNet review: 2161170
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we present a generalized Kakutani-Kodaira theorem for all locally compact groups.

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

  • 1. W. W. Comfort, Topological groups, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 1143–1263. MR 776643
  • 2. Michel Enock and Jean-Marie Schwartz, Kac algebras and duality of locally compact groups, Springer-Verlag, Berlin, 1992. With a preface by Alain Connes; With a postface by Adrian Ocneanu. MR 1215933
  • 3. F. P. Greenleaf and M. Moskowitz, Cyclic vectors for representations associated with positive definite measures: nonseparable groups, Pacific J. Math. 45 (1973), 165–186. MR 0349896
  • 4. Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773
  • 5. Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
  • 6. Karl H. Hofmann and Sidney A. Morris, The structure of compact groups, de Gruyter Studies in Mathematics, vol. 25, Walter de Gruyter & Co., Berlin, 1998. A primer for the student—a handbook for the expert. MR 1646190
  • 7. Zhiguo Hu, On the set of topologically invariant means on the von Neumann algebra 𝑉𝑁(𝐺), Illinois J. Math. 39 (1995), no. 3, 463–490. MR 1339838
  • 8. Z. Hu, Maximally decomposable von Neumann algebras on locally compact groups and duality, Preprint, 2004.
  • 9. Shizuo Kakutani and Kunihiko Kodaira, Über das Haarsche Mass in der lokal bikompakten Gruppe, Proc. Imp. Acad. Tokyo 20 (1944), 444–450 (German). MR 0014401
  • 10. Anthony To Ming Lau and Viktor Losert, Complementation of certain subspaces of 𝐿_{∞}(𝐺) of a locally compact group, Pacific J. Math. 141 (1990), no. 2, 295–310. MR 1035445

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 22D05

Retrieve articles in all journals with MSC (2000): 22D05

Additional Information

Zhiguo Hu
Affiliation: Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada N9B 3P4

Keywords: Locally compact groups, cardinal invariants of locally compact groups, the Kakutani-Kodaira Theorem
Received by editor(s): November 27, 2003
Received by editor(s) in revised form: June 22, 2004
Published electronically: May 9, 2005
Additional Notes: This research was supported by an NSERC grant.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.