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.
@article{bwmeta1.element.doi-10_1515_math-2015-0070,
author = {Massoud Amini},
title = {Module Connes amenability of hypergroup measure algebras},
journal = {Open Mathematics},
volume = {13},
year = {2015},
zbl = {06433979},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0070}
}
Massoud Amini. Module Connes amenability of hypergroup measure algebras. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0070/
[1] Runde, V., Amenability for dual Banach algebras, Studia Math., 2001, 148, 47-66. | Zbl 1003.46028
[2] Runde, V., Connes-amenability and normal, virtual diagonals for measure algebras, J. London Math. Soc., 2003, 67, 643-656. [Crossref] | Zbl 1040.22002
[3] Runde, V., Connes-amenability and normal, virtual diagonals for measure algebras II, Bull. Austral. Math. Soc., 2003, 68, 325-328. [Crossref] | Zbl 1042.22001
[4] Runde, V., Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand., 2004, 95, 124-144. | Zbl 1087.46035
[5] Johnson, B.E., Kadison, R.V., Ringrose, J., Cohomology of operator algebras III, Bull. Soc. Math. France, 1972, 100, 73-79. | Zbl 0234.46066
[6] Jewett, R.I., Spaces with an abstract convolution of measures, Advances in Math., 1975, 18, 1-110. | Zbl 0325.42017
[7] Bloom, W.R., Heyer, H., Harmonic Analysis of Probability Measures on Hypergroups, Walter de Gruyter, Berlin, 1995. | Zbl 0828.43005
[8] Amini, M., Module amenability for semigroup algebras, Semigroup Forum, 2004, 69, 243-254. | Zbl 1059.43001
[9] M. A. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Func. Anal., 1967, 1, 443-491. | Zbl 0181.41303
[10] Daws, M., Dual Banach algebras: representations and injectivity, Studia Math., 2007, 178(3), 231-275. | Zbl 1115.46038
[11] Ryan, R., Introduction to Tensor Products of Banach Spaces, Springer-Verlag, London, 2002.
[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. | Zbl 0920.46038
[13] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc., 1951, 71, 152-182. | Zbl 0043.37902
[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. [Crossref] | Zbl 0937.33009
[15] Grothendieck, A., Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math., 1953, 74, 168-186. [Crossref] | Zbl 0046.11702
[16] M. Skantharajah, Amenable hypergroups, Illinois J. Math., 1992, 36(1), 15-46. | Zbl 0755.43003
[17] Johnson, B.E., Separate continuity and measurability, Proc. Amer. Math. Soc., 1969, 20, 420-422. [Crossref] | Zbl 0181.14502
[18] Lasser, R., Amenability and weak amenability of `1-algebras of polynomial hypergroups, Studia Math., 2007, 182, 183-196. | Zbl 1126.43003
[19] Lasser, R., Various amenability properties of the L1-algebra of polynomial hypergroups and applications, J. Comput. Appl. Math., 2009, 233, 786-792. [WoS] | Zbl 1182.43008
[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. [Crossref][WoS] | Zbl 1200.43001
[21] Runde V., Lectures on Amenability, Lecture Notes in Mathematics 1774, Springer-Verlag, Berlin, 2002. | Zbl 0999.46022
[22] Doran, R.S., Wichman, J., Approximate Identities and Factorization in Banach Modules, Lecture Notes in Mathematics 768, Springer-Verlag, Berlin, 1979.
[23] Lasser, R., Orthogonal polynomials and hypergroups, Rend. Mat., 1983, 3, 185-209. | Zbl 0538.33010