Biflatness and Pseudo-Amenability of Segal Algebras
Canadian journal of mathematics, Tome 62 (2010) no. 4, pp. 845-869

Voir la notice de l'article provenant de la source Cambridge University Press

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, ${{L}^{1}}\left( G \right)$ , and the Fourier algebra, $A\left( G \right)$ , of a locally compact group $G$ .
DOI : 10.4153/CJM-2010-044-4
Mots-clés : 43A20, 43A30, 46H25, 46H10, 46H20, 46L07, Segal algebra, pseudo-amenable Banach algebra, biflat Banach algebra
Samei, Ebrahim; Spronk, Nico; Stokke, Ross. Biflatness and Pseudo-Amenability of Segal Algebras. Canadian journal of mathematics, Tome 62 (2010) no. 4, pp. 845-869. doi: 10.4153/CJM-2010-044-4
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[1] [1] Aristov, O. Y., Runde, V., and Spronk, N., Operator biflatness of the Fourier algebra and approximate indicators for subgroups. J. Funct. Anal. 209(2004), no. 2, 367–387. doi:10.1016/S0022-1236(03)00169-1 Google Scholar

[2] [2] Burnham, J. T., Closed ideals in subalgebras of Banach algebras. I. Proc. Amer. Math. Soc. 32(1972), 551–555. doi:10.2307/2037857 Google Scholar

[3] [3] Curtis, P. C., Loy, R. J., The structure of amenable Banach algebras. J. London Math. Soc. (2) 40(1989), no. 1, 89–104. doi:10.1112/jlms/s2-40.1.89 Google Scholar

[4] [4] Dales, H. G., Banach algebras and automatic continuity. London Mathematical Society Monographs, 24, The Clarendon Press, Oxford University Press, New York, 2000. Google Scholar

[5] [5] Dales, H. G., Ghahramani, F., and Helemskii, A. Ya., The amenability of measure algebras. J. London Math. Soc. (2) 66(2002), no. 1, 213–226. doi:10.1112/S0024610702003381 Google Scholar

[6] [6] Effros, E. G. and Ruan, Z.-J., Operator spaces. London Mathematical Society Monographs, 23, The Clarendon Press, Oxford University Press, New York, 2000. Google Scholar

[7] [7] Eymard, P., L’algèbre de Fourier d’un groupe localement compact. Bull. Soc. Math. France 92(1964), 181–236. Google Scholar

[8] [8] Forrest, B. and Wood, P., Cohomology and the operator space structure of the Fourier algebra and its second dual. Indiana Univ. Math. J. 50(2001), no. 3, 1217–1240. doi=10.1512/iumj.2001.50.1835 Google Scholar

[9] [9] Forrest, B. E. and Runde, V., Amenability and weak amenability of the Fourier algebra. Math. Z. 250(2005), 731–744. doi:10.1007/s00209-005-0772-2 Google Scholar

[10] [10] Forrest, B. E., Spronk, N., and Wood, P. J., Operator Segal algebras in Fourier algebras. Studia Math. 179(2007), no. 3, 277–295. doi:10.4064/sm179-3-5 Google Scholar

[11] [11] Ghahramani, F. and Lau, A. T.-M., Weak amenability of certain classes of Banach algebras without bounded approximate identities. Math. Proc. Cambridge Philos. Soc. 133(2002), no. 2, 357–371. doi=10.1017/S0305004102005960 Google Scholar

[12] [12] Ghahramani, F. and Lau, A. T.-M., Approximate weak amenability, derivations and Arens regularity of Segal algebras. Studia Math.169(2005), no. 2, 189–205. doi:10.4064/sm169-2-6 Google Scholar

[13] [13] Ghahramani, F. and Loy, R. J., Generalized notions of amenability. J. Funct. Anal. 208(2004), no. 1, 229–260. doi:10.1016/S0022-1236(03)00214-3 Google Scholar

[14] [14] Ghahramani, F. and Stokke, R., Approximate and pseudo-amenability of the Fourier algebra. Indiana Univ. Math. J. 56(2007), no. 2, 909–930. doi:10.1512/iumj.2007.56.2951 Google Scholar

[15] [15] Ghahramani, F. and Zhang, Y., Pseudo-amenable and pseudo-contractible Banach algebras. Math. Proc. Cambridge Philos. Soc. 142(2007), no. 1, 111–123. doi:10.1017/S0305004106009649 Google Scholar

[16] [16] Helemskii, A. Ya., Banach and locally convex algebras. The Clarendon Press, Oxford University Press, New York, 1993. Google Scholar

[17] [17] Johnson, B. E., Cohomology in Banach algebras. Memoirs of the American Mathematical Society, 127, American Mathematical Society, Providence, RI, 1972. Google Scholar

[18] [18] Johnson, B. E., Approximate diagonals and cohomology of certain annihilator Banach algebras. Amer. J. Math. 94(1972), 685–698. doi:10.2307/2373751 Google Scholar

[19] [19] Johnson, B. E., Non-amenability of the Fourier algebra of a compact group. J. London Math. Soc. (2) 50(1994), no. 2, 361–374. Google Scholar

[20] [20] Kelley, J. L., General topology. D. Van Nostrand Company, Inc., Toronto–New York–London, 1955. Google Scholar

[21] [21] Kotzmann, E. and Rindler, H., Segal algebras on non-abelian groups. Trans. Amer. Math. Soc. 237(1978), 271–281. doi:10.2307/1997622 Google Scholar

[22] [22] Paterson, A. L. T., Amenability. Mathematical Surveys and Monographs, 29, American Mathematical Society, Providence, RI, 1988. Google Scholar

[23] [23] Pirkovskii, A. Yu., Approximate characterizations of projectivity and injectivity for Banach modules. Math. Proc. Cambridge Philos. Soc. 143(2007), no. 2, 375–385. doi=10.1017/S0305004107000163 Google Scholar

[24] [24] Pisier, G., Introduction to operator space theory. London Mathematical Society Lecture Note Series, 294, Cambridge University Press, Cambridge, 2003. Google Scholar

[25] [25] Renaud, P. F., Invariant means on a class of von Neumann algebras. Trans. Amer. Math. Soc. 170(1972), 285–291. doi:10.2307/1996311 Google Scholar

[26] [26] Reiter, H. and Stegeman, J. D., Classical Harmonic Analysis and locally compact groups. Second ed., London Mathematical Society Monographs, 22, The Clarendon Press, Oxford University Press, New York, 2000. Google Scholar

[27] [27] Ruan, Z.-J., The operator amenability of A(G). Amer. J. Math. 117(1995), no. 6, 1449–1474. doi:10.2307/2375026 Google Scholar

[28] [28] Ruan, Z.-J., Connes-amenability and normal, virtual diagonals for measure algebras. I. J. London Math. Soc. (2) 67(2003), no. 3, 643–656. doi:10.1112/S0024610703004125 Google Scholar

[29] [29] Spronk, N., Operator space structure on Feichtinger's Segal algebra. J. Funct. Anal. 248(2007), no. 1, 152–174. doi:10.1016/j.jfa.2007.03.028 Google Scholar

[30] [30] Takesaki, M. and Tatsuuma, N., Duality and subgroups. II. J. Funct. Anal. 11(1972), 184–190. doi:10.1016/0022-1236(72)90087-0 Google Scholar

[31] [31] Wood, P. J., The operator biprojectivity of the Fourier algebra. Canad. J. Math. 54(2002), no. 5, 1100–1120. Google Scholar

[32] [32] Zhang, Y., Nilpotent ideals in a class of Banach algebras. Proc. Amer. Math. Soc. 127(1999), no. 11, 3237–3242. doi:10.1090/S0002-9939-99-04896-0 Google Scholar

[33] [33] Zhang, Y., Approximate identities for ideals of Segal algebras on a compact group. J. Funct. Anal. 191(2002), no. 1, 123–131. doi:10.1006/jfan.2001.3872 Google Scholar

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