Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

1 Issue per year


IMPACT FACTOR 2017: 0.831
5-year IMPACT FACTOR: 0.836

CiteScore 2017: 0.68

SCImago Journal Rank (SJR) 2017: 0.450
Source Normalized Impact per Paper (SNIP) 2017: 0.829

Mathematical Citation Quotient (MCQ) 2017: 0.32

Open Access
Online
ISSN
2391-5455
See all formats and pricing
More options …
Volume 13, Issue 1

Issues

Volume 13 (2015)

Module Connes amenability of hypergroup measure algebras

Massoud Amini
  • Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O.Box 14115-134, Tehran , Iran
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-10-28 | DOI: https://doi.org/10.1515/math-2015-0070

Abstract

We define the concept of module Connes amenability for dual Banach algebras which are also Banach modules with a compatible action. We distinguish a closed subhypergroup K0 of a locally compact measured hypergroup K, and show that, under different actions, amenability of K, M.K0/-module Connes amenability of M.K/, and existence of a normal M.K0/-module virtual diagonal are related.

Keywords: Hypergroup; Module Connes amenability; Normal module virtual diagonal

References

  • [1] Runde, V., Amenability for dual Banach algebras, Studia Math., 2001, 148, 47-66. Google Scholar

  • [2] Runde, V., Connes-amenability and normal, virtual diagonals for measure algebras, J. London Math. Soc., 2003, 67, 643-656. CrossrefGoogle Scholar

  • [3] Runde, V., Connes-amenability and normal, virtual diagonals for measure algebras II, Bull. Austral. Math. Soc., 2003, 68, 325-328. CrossrefGoogle Scholar

  • [4] Runde, V., Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand., 2004, 95, 124-144. Google Scholar

  • [5] Johnson, B.E., Kadison, R.V., Ringrose, J., Cohomology of operator algebras III, Bull. Soc. Math. France, 1972, 100, 73-79. Google Scholar

  • [6] Jewett, R.I., Spaces with an abstract convolution of measures, Advances in Math., 1975, 18, 1-110. Google Scholar

  • [7] Bloom, W.R., Heyer, H., Harmonic Analysis of Probability Measures on Hypergroups, Walter de Gruyter, Berlin, 1995. Google Scholar

  • [8] Amini, M., Module amenability for semigroup algebras, Semigroup Forum, 2004, 69, 243-254. Google Scholar

  • [9] M. A. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Func. Anal., 1967, 1, 443-491. Google Scholar

  • [10] Daws, M., Dual Banach algebras: representations and injectivity, Studia Math., 2007, 178(3), 231-275. Google Scholar

  • [11] Ryan, R., Introduction to Tensor Products of Banach Spaces, Springer-Verlag, London, 2002. Google Scholar

  • [12] Corach, G., Galé, J. E., Averaging with virtual diagonals and geometry of representations. In: Banach algebras ’97, Walter de Grutyer, Berlin, 87-100, 1998. Google Scholar

  • [13] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc., 1951, 71, 152-182. Google Scholar

  • [14] T. H. Koornwinder, Alan L. Schwartz, Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle, Constr. Approx., 1997, 13, 537-567. CrossrefGoogle Scholar

  • [15] Grothendieck, A., Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math., 1953, 74, 168-186. CrossrefGoogle Scholar

  • [16] M. Skantharajah, Amenable hypergroups, Illinois J. Math., 1992, 36(1), 15-46. Google Scholar

  • [17] Johnson, B.E., Separate continuity and measurability, Proc. Amer. Math. Soc., 1969, 20, 420-422. CrossrefGoogle Scholar

  • [18] Lasser, R., Amenability and weak amenability of `1-algebras of polynomial hypergroups, Studia Math., 2007, 182, 183-196. Google Scholar

  • [19] Lasser, R., Various amenability properties of the L1-algebra of polynomial hypergroups and applications, J. Comput. Appl. Math., 2009, 233, 786-792. Web of ScienceGoogle Scholar

  • [20] Amini, M., Bodaghi, A., Ebrahimi Bagha, D., Module amenability of the second dual and module topological center of semigroup algebras, Semigroup Forum, 2010, 80, 302-312. Web of ScienceCrossrefGoogle Scholar

  • [21] Runde V., Lectures on Amenability, Lecture Notes in Mathematics 1774, Springer-Verlag, Berlin, 2002. Google Scholar

  • [22] Doran, R.S., Wichman, J., Approximate Identities and Factorization in Banach Modules, Lecture Notes in Mathematics 768, Springer-Verlag, Berlin, 1979. Google Scholar

  • [23] Lasser, R., Orthogonal polynomials and hypergroups, Rend. Mat., 1983, 3, 185-209. Google Scholar

About the article

Received: 2015-01-15

Accepted: 2015-10-14

Published Online: 2015-10-28


Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0070.

Export Citation

©2015 Massoud Amini. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in