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Operator Connes-amenability of completely bounded multiplier Banach algebras. (English) Zbl 07088756
Let \(B\) be a completely contractive Banach algebra and \({\mathcal{M}}_{cb}(B)\) the completely bounded multiplier algebra of \(B\). Conditions, under which a) \({\mathcal{M}}_{cb}(B)\) is a dual Banach algebra and b) the operator amenability of \(B\) is equivalent to the operator Connes-amenability of \({\mathcal{M}}_{cb}(B)\), are found.
Reviewer: Mati Abel (Tartu)
46H20 Structure, classification of topological algebras
46H35 Topological algebras of operators
Full Text: DOI
[1] Daws, M., Connes-amenability of bidual and weighted semigroup algebras, Math. Scand. 99 (2006), 217-246
[2] Daws, M., Multipliers, self-induced and dual Banach algebras, Dissertationes Math. (Rozprawy Mat.) 470 (2010), 62 pp
[3] Deutsch, E., Matricial norms, Numer. Math. 19 (1) (1970), 73-84
[4] Effros, E. G.; Ruan, Z.-J., Operator Spaces, Clarendon Press, 2000
[5] Hayati, B.; Amini, M., Connes-amenability of multiplier Banach algebras, Kyoto J. Math. 50 (2010), 41-50
[6] Hayati, B.; Amini, M., Dual multiplier Banach algebras and Connes-amenability, Publ. Math. Debrecen 86 (2015), 169-182
[7] Helmeskii, A. Ya., Homological essence of amenability in the sense of A. Connes: the injectivity of the predual bimodule, Math. USSR.-Sb. 68 (1991), 555-566
[8] Johnson, B. E., An introduction to the theory of centralizers, Proc. London Math. Soc. 14 (1964), 299-320
[9] Johnson, B. E., Cohomology in Banach Algebras, Mem. Amer. Math. Soc. 127 (1972)
[10] Johnson, B. E., Non-amenability of the Fourier algebra of a compact group, J. London Math. Soc. 50 (2) (1994), 361-374
[11] Johnson, B. E.; Kadison, R. V.; Ringrose, J. R., Cohomology of operator algebras III, Bull. Soc. Math. France 100 (1972), 73-96
[12] Larsen, R., An Introduction to the Theory of Mutipliers, Springer-Verlag, Berlin, 1971
[13] Oshobi, E. O.; Pym, J. S., Banach algebras whose duals consist of multipliers, Math. Proc. Cambridge Philos. Soc. 102 (1987), 481-505
[14] Ruan, Z.-J., The operator amenability of \(A(G)\), Amer. J. Math. 117 (1995), 1449-1474
[15] Runde, V., Amenability for dual Banach algebras, Studia Math. 148 (2001), 47-66
[16] Runde, V., Lectures on Amenability, Lecture Notes in Math., vol. 1774, Springer-Verlag, Berlin-Heidelberg-New York, 2002
[17] Runde, V., Connes-amenability and normal, virtual diagonals for measure algebras. I, J. London Math. Soc. 67 (2003), 643-656
[18] Runde, V., Connes-amenability and normal, virtual diagonals for measure algebras. II, Bull. Austral. Math. Soc. 68 (2003), 325-328
[19] Runde, V., Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand. 95 (2004), 124-144
[20] Runde, V.; Spronk, N., Operator amenability of Fourier-Stieltjes algebras, Math. Proc. Cambridge Philos. Soc. 136 (2004), 675-686
[21] Runde, V.; Uygul, F., Connes-amenability of Fourier-Stieltjes algebras, Bull. London Math. Soc. (2015)
[22] Spronk, N., Measurable Schur multiplies and completely bounded multipliers of the Fourier algebras, Proc. London Math. Soc. 89 (2004), 161-192
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