On Fourier algebra of a locally compact hypergroup

Abstract

We give sufficient conditions for the Fourier and the Fourier-Stieltjes spaces of a locally compact hypergroup to be Banach algebras.

Key words: Fourier algebra, Fourier-Stieltjes algebra, DJS-hypergroup, locally compact hypergroup, dual algebras, Pontryagin duality.

Full Text

Article Information

Title	On Fourier algebra of a locally compact hypergroup
Source	Methods Funct. Anal. Topology, Vol. 21 (2015), no. 3, 246-255
MathSciNet	MR3521695
zbMATH	06630271
Milestones	Received 26/05/2015
Copyright	The Author(s) 2015 (CC BY-SA)

Authors Information

A. A. Kalyuzhnyi
Institute of Mathematics, National Academy of Sciences of Ukraine, vul. Tereshchinkivs’ka, 3, Kyiv, 01601, Ukraine

G. B. Podkolzin
Ukrainian National Technical University (“KPI”), pr. Pobedy, 57, Kyiv, Ukraine

Yu. A. Chapovsky
Institute of Mathematics, National Academy of Sciences of Ukraine, vul. Tereshchinkivs’ka, 3, Kyiv, 01601, Ukraine

Citation Example

A. A. Kalyuzhnyi, G. B. Podkolzin, and Yu. A. Chapovsky, On Fourier algebra of a locally compact hypergroup, Methods Funct. Anal. Topology 21 (2015), no. 3, 246-255.

BibTex

@article {MFAT835,
    AUTHOR = {A. A. Kalyuzhnyi and G. B. Podkolzin and Yu. A. Chapovsky},
     TITLE = {On Fourier algebra of a locally compact hypergroup},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {21},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {246-255},
      ISSN = {1029-3531},
  MRNUMBER = {MR3521695},
 ZBLNUMBER = {06630271},
       URL = {http://mfat.imath.kiev.ua/article/?id=835},
}

References

1. Pierre Eymard, Lalg\`ebre de Fourier dun groupe localement compact, Bull. Soc. Math. France 92 (1964), 181-236.  MathSciNet
2. Varadharajan Muruganandam, Fourier algebra of a hypergroup. I, J. Aust. Math. Soc. 82 (2007), no. 1, 59-83.  MathSciNet CrossRef
3. Varadharajan Muruganandam, Fourier algebra of a hypergroup. II. Spherical hypergroups, Math. Nachr. 281 (2008), no. 11, 1590-1603.  MathSciNet CrossRef
4. N. Bourbaki, Integration, vol. 1, Springer-Verlag, Berlin-Heidelberg, 2004.
5. Walter R. Bloom, Herbert Heyer, Harmonic analysis of probability measures on hypergroups, Walter de Gruyter \& Co., Berlin, 1995.  MathSciNet CrossRef
6. Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979.  MathSciNet
7. Gert K. Pedersen, $C^\ast $-algebras and their automorphism groups, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979.  MathSciNet
8. Forrest W. Stinespring, Positive functions on $C^ *$-algebras, Proc. Amer. Math. Soc. 6 (1955), 211-216.  MathSciNet
9. Jacques Dixmier, Les $C^\ast $-alg\`ebres et leurs representations, Gauthier-Villars \'Editeur, Paris, 1969.  MathSciNet