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Approximate Amenability of Segal Algebras II

Published online by Cambridge University Press:  20 November 2018

Mahmood Alaghmandan*
Affiliation:
(Former Address) Fields Institute for Research in Mathematical Sciences, 222 College St., Toronto, ON M5T 3J1(Current Adress) Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1. e-mail: mahmood.a@uwaterloo.ca
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Abstract

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We prove that no proper Segal algebra of a SIN group is approximately amenable.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2015

References

[1] Alaghmandan, M., Approximate amenability of Segal algebras. J. Aust. Math. Soc. 95 (2013), no. 1, 2035. http://dx.doi.org/10.1017/S1446788713000256 Google Scholar
[2] Burnham, J. T., Closed ideals in subalgebras of Banach algebras. I. Proc. Amer. Math. Soc. 32 (1972), 551555. http://dx.doi.org/10.1090/S0002-9939-1972-0295078-5 Google Scholar
[3] Choi, Y. and Ghahramani, F., Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras. Q. J. Math. 62 (2011), no. 1, 3958. http://dx.doi.org/10.1093/qmath/hap034 Google Scholar
[4] Choi, Y., Ghahramani, F., and Zhang, Y., Approximate and pseudo-amenability of various classes of Banach algebras. J. Funct. Anal. 256 (2009), no. 10, 31583191. http://dx.doi.org/10.1016/j.jfa.2009.02.012 Google Scholar
[5] Dales, H. G. and Loy, R. J., Approximate amenability of semigroup algebras and Segal algebras. Dissertationes Math. (Rozprawy Mat.), 474 (2010) .Google Scholar
[6] Ghahramani, F. and Loy, R. J., Generalized notions of amenability. J. Funct. Anal. 208 (2004), no. 1, 229260. http://dx.doi.org/10.1016/S0022-1236(03)00214-3 Google Scholar
[7] Ghahramani, F., Loy, R. J., and Y. Zhang, Generalized notions of amenability. II. J. Funct. Anal. 254 (2008), no. 7, 17761810. http://dx.doi.org/10.1016/j.jfa.2007.12.011 Google Scholar
[8] Kaniuth, E., A course in commutative Banach algebras. Graduate Texts in Mathematics, 246, Springer, New York, 2009.Google Scholar
[9] Kotzmann, E. and Rindler, H., Segal algebras on non-abelian groups. Trans. Amer. Math. Soc. 237 (1978), 271281. http://dx.doi.org/10.1090/S0002-9947-1978-0487277-4 Google Scholar
[10] Liukkonen, J. and Mosak, R., Harmonic analysis and centers of group algebras. Trans. Amer. Math. Soc. 195 (1974), 147163. http://dx.doi.org/10.1090/S0002-9947-1974-0350322-7 Google Scholar
[11] Reiter, H., L1-algebras and Segal algebras. Lecture Notes in Mathematics, 231, Springer-Verlag, Berlin, 1971.Google Scholar