Annals of Functional Analysis

Approximate amenability and contractibility of hypergroup algebras

J. Laali and R. Ramezani

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Let K be a hypergroup. The purpose of this article is to study the notions of amenability of the hypergroup algebras L(K), M(K), and L(K). Among other results, we obtain a characterization of approximate amenability of L(K). Moreover, we introduce the Banach space L(K,L(K)) and prove that the dual of a Banach hypergroup algebra L(K) can be identified with L(K,L(K)). In particular, L(K) is an F-algebra. By using this fact, we give necessary and sufficient conditions for K to be left-amenable.

Article information

Ann. Funct. Anal., Volume 9, Number 4 (2018), 551-565.

Received: 16 October 2017
Accepted: 7 January 2018
First available in Project Euclid: 10 October 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A62: Hypergroups
Secondary: 46K05: General theory of topological algebras with involution 43A07: Means on groups, semigroups, etc.; amenable groups

hypergroup approximate amenability involution left-amenable


Laali, J.; Ramezani, R. Approximate amenability and contractibility of hypergroup algebras. Ann. Funct. Anal. 9 (2018), no. 4, 551--565. doi:10.1215/20088752-2018-0001.

Export citation


  • [1] M. Amini and A. R. Medghalchi, Amenability of compact hypergroup algebras, Math. Nachr 287 (2014), no. 14–15, 1609–1617.
  • [2] W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, De Gruyter Stud. Math. 20, De Gruyter, Berlin, 1995.
  • [3] H. G. Dales, Banach Algebras and Automatic Continuity, London Math. Soc. Monogr. (N.S.) 24, Oxford Univ. Press, New York, 2000.
  • [4] C. F. Dunkl, The measure algebra of a locally compact hypergroup, Trans. Amer. Math. Soc. 179 (1973), 331–348.
  • [5] F. Ghahramani and R. J. Loy, Generalized notions of amenability, J. Funct. Anal. 208 (2004), no. 1, 229–260.
  • [6] F. Ghahramani, R. J. Loy, and G. A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc. 124 (1996), no. 5, 1489–1497.
  • [7] F. Ghahramani, R. J. Loy, and Y. Zhang, Generalized notions of amenability, II, J. Funct. Anal. 254 (2008), no. 7, 1776–1810.
  • [8] F. Ghahramani and A. R. Medghalchi, Compact multipliers on weighted hypergroup algebras, Math. Proc. Cambridge Philos. Soc. 98 (1985), no. 3, 493–500.
  • [9] F. Ghahramani and Y. Zhang, Pseudo-amenable and pseudo-contractible Banach algebras, Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 1, 111–123.
  • [10] Z. Hu, M. S. Monfared, and T. Traynor, On character amenable Banach algebras, Studia Math. 193 (2009), no. 1, 53–78.
  • [11] R. I. Jewett, Spaces with an abstract convolution of measures, Adv. Math. 18 (1975), no. 1, 1–101.
  • [12] E. Kaniuth, A. T. Lau, and J. Pym, On $\varphi$-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 1, 85–96.
  • [13] R. Lasser, Various amenability properties of the $L^{1}$-algebra of polynomial hypergroups and applications, J. Comput. Appl. Math. 233 (2009), no. 3, 786–792.
  • [14] A. T. Lau, Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups, Fund. Math. 118 (1983), no. 3, 161–175.
  • [15] A. T. Lau and A. Ülger, Topological centers of certain dual algebras, Trans Amer. Math. Soc. 394, no. 3 (1996), 1191–1212.
  • [16] A. R. Medghalchi, The second dual algebra of a hypergroup, Math. Z. 210 (1992), no. 4, 615–624.
  • [17] A. R. Medghalchi, Cohomology on hypergroup algebras, Studia Sci. Math. Hungar. 39 (2002), no. 3-4, 297–307.
  • [18] A. R. Medghalchi and S. M. S. Modarres, Amenability of the second dual of hypergroup algebras, Acta Math. Hungar. 86 (2000), no. 4, 335–342.
  • [19] G. J. Murphy, $C^{*}$-Algebras and Operator Theory, Academic Press, Boston, 1990.
  • [20] W. Rudin, Functional Analysis, 2nd ed., Internat. Ser. Pure Appl. Math., McGraw-Hill, New York, 1991.
  • [21] S. Sakai, $C^{*}$-algebras and $W^{*}$-algebras, Ergeb. Math. Grenzgeb. (3) 60, Springer, New York, 1971.
  • [22] M. Skantharajah, Amenable hypergroups, Illinois J. Math. 36 (1992), no. 1, 15–46.