Abstract
Given a Banach algebra A, with an amenable ideal I and amenable quotient A/I, we seek for relations among the amenability constants of A, A/I and I. We also provide some examples as applications. In particular, we propose a suitable approach to the amenability constant of A #. Finally, we give an upper bound for the amenability constant of the augmentation ideal L 10 (G) of an amenable σ-compact group G.
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References
Johnson B. E., Cohomology on Banach Algebras, Amer. Math. Soc., Providence RI (1972) (Mem. Amer. Math. Soc.; 127).
Johnson B. E., “Approximate diagonals and cohomology of certain annihilator Banach algebras,” Amer. J. Math., 94, 685–698 (1972).
Runde V., Lectures on Amenability, Springer-Verlag, Berlin (2002) (Lecture Notes Math.; V. 1774).
Johnson B. E., “Non-amenability of the Fourier algebra of a compact group,” J. London Math. Soc. (2), 50, No. 2, 361–374 (1994).
Runde V., “The amenability constant of the Fourier algebra,” Proc. Amer. Math. Soc., 134, No. 5, 1473–1481 (2006).
Dales H. G., Lau A. T.-M., and Strauss D., Banach Algebras on Semigroups and on Their Compactifications, Amer. Math. Soc., Providence, RI (2010) (Mem. Amer. Math. Soc.; V. 205, No. 966).
Duncan J. and Paterson A. L. T., “Amenability for discrete convolution semigroup algebras,” Math. Scand., 66, 141–146 (1990).
Stokke R., “Approximate diagonals and Folner conditions for amenable groups and semigroups,” Stud. Math., 164, 139–159 (2004).
Dales H. G., Banach Algebras and Automatic Continuity, Clarendon Press, Oxford (2000) (London Math. Soc. Monogr., V. 24).
Heagerup U., “All nuclear C*-algebras are amenable,” Invent. Math., 74, No. 2, 305–319 (1983).
Ghahramani F. and Loy R. J., “Generalized notions of amenability,” J. Funct. Anal., 208, 229–260 (2004).
Bonsall F. F. and Duncan J., Complete Normed Algebras, Springer-Verlag, Berlin (1973).
Willis G. A., “Probability measures on groups and some related ideals in group algebras,” J. Funct. Anal., 92, 202–263 (1990).
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Original Russian Text Copyright © 2014 Soroushmehr M.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 6, pp. 1391–1395, November–December, 2014.
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Soroushmehr, M. A note on the amenability constant of Banach algebras. Sib Math J 55, 1133–1136 (2014). https://doi.org/10.1134/S0037446614060160
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DOI: https://doi.org/10.1134/S0037446614060160