Module Connes amenability of hypergroup measure algebras

• Autorzy: Massoud Amini
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hypergroup; Module Connes amenability; Normal module virtual diagonal

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-01-15

zaakceptowano

2015-10-14

online

2015-10-28

Twórcy

autor

Massoud Amini

• Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares
  University, P.O.Box 14115-134, Tehran , Iran

Bibliografia

• [1] Runde, V., Amenability for dual Banach algebras, Studia Math., 2001, 148, 47-66.
• [2] Runde, V., Connes-amenability and normal, virtual diagonals for measure algebras, J. London Math. Soc., 2003, 67, 643-656. [Crossref]
• [3] Runde, V., Connes-amenability and normal, virtual diagonals for measure algebras II, Bull. Austral. Math. Soc., 2003, 68, 325-328. [Crossref]
• [4] Runde, V., Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand., 2004, 95, 124-144.
• [5] Johnson, B.E., Kadison, R.V., Ringrose, J., Cohomology of operator algebras III, Bull. Soc. Math. France, 1972, 100, 73-79.
• [6] Jewett, R.I., Spaces with an abstract convolution of measures, Advances in Math., 1975, 18, 1-110.
• [7] Bloom, W.R., Heyer, H., Harmonic Analysis of Probability Measures on Hypergroups, Walter de Gruyter, Berlin, 1995.
• [8] Amini, M., Module amenability for semigroup algebras, Semigroup Forum, 2004, 69, 243-254.
• [9] M. A. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Func. Anal., 1967, 1, 443-491.
• [10] Daws, M., Dual Banach algebras: representations and injectivity, Studia Math., 2007, 178(3), 231-275.
• [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.
• [13] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc., 1951, 71, 152-182.
• [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]
• [15] Grothendieck, A., Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math., 1953, 74, 168-186. [Crossref]
• [16] M. Skantharajah, Amenable hypergroups, Illinois J. Math., 1992, 36(1), 15-46.
• [17] Johnson, B.E., Separate continuity and measurability, Proc. Amer. Math. Soc., 1969, 20, 420-422. [Crossref]
• [18] Lasser, R., Amenability and weak amenability of `1-algebras of polynomial hypergroups, Studia Math., 2007, 182, 183-196.
• [19] Lasser, R., Various amenability properties of the L1-algebra of polynomial hypergroups and applications, J. Comput. Appl. Math., 2009, 233, 786-792. [WoS]
• [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]
• [21] Runde V., Lectures on Amenability, Lecture Notes in Mathematics 1774, Springer-Verlag, Berlin, 2002.
• [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.

Identyfikatory

DOI

10.1515/math-2015-0070