Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T17:28:40.491Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximate Amenability of Segal Algebras II

Published online by Cambridge University Press:  20 November 2018

Mahmood Alaghmandan
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: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Keywords

46H2043A20Segal algebrasapproximate amenabilitySIN groupscommutative Banach algebras
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 3 - 6
Copyright
Copyright © Canadian Mathematical Society 2015

References

[1] Alaghmandan, M., Approximate amenability of Segal algebras. J. Aust. Math. Soc. 95 (2013), no. 1, 20–35. 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), 551–555. 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, 39–58. 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, 3158–3191. 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, 229–260. 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, 1776–1810. 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), 271–281. 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), 147–163. 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