Semigroup Forum

, Volume 79, Issue 2, pp 349–354 | Cite as

A note on the approximate amenability of semigroup algebras

Research article
First Online:
Received:
Accepted:

Abstract

It is known that the bicyclic semigroup S 1 is an amenable inverse semigroup. In this note we show that the convolution semigroup algebra ℓ 1(S 1) is not approximately amenable.

Keywords

Approximately amenable Banach algebra Bicyclic semigroup Derivation 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berglund, J.F., Junghenn, H.D., Milnes, P.: Analysis on Semigroups. Wiley, New York (1988) Google Scholar
  2. 2.
    Bowling, S., Duncan, J.: First order cohomology of Banach semigroup algebras. Semigroup Forum 56, 130–145 (1998) MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Choi, Y., Ghahramani, F., Zhang, Y.: Approximate and pseudo-amenability of various algebras. J. Funct. Anal. (to appear) Google Scholar
  4. 4.
    Dales, H.G., Lau, A.T.-M., Strauss, D.: Banach Algebras on Semigroups and their Compactifications. Mem. Am. Math. Soc. (to appear) Google Scholar
  5. 5.
    Duncan, J., Namioka, I.: Amenability of inverse semigroups and their semigroup algebras. Proc. R. Soc. Edinb. A 80, 309–321 (1978) MATHMathSciNetGoogle Scholar
  6. 6.
    Duncan, J., Paterson, A.L.T.: Amenability for discrete convolution semigroup algebras. Math. Scand. 66, 141–146 (1990) MATHMathSciNetGoogle Scholar
  7. 7.
    Ghahramani, F., Loy, R.J.: Generalized notions of amenability. J. Funct. Anal. 208, 229–260 (2004) MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Ghahramani, F., Loy, R.J., Zhang, Y.: Generalized notions of amenability II. J. Funct. Anal. 254, 1776–1810 (2008) MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Gronbaek, N.: A characterization of weak amenability. Stud. Math. 94, 149–162 (1987) MathSciNetGoogle Scholar
  10. 10.
    Gronbaek, N.: Amenability of weighted discrete semigroup convolution algebras. Proc. R. Soc. Edinb. A 110, 351–360 (1998) MathSciNetGoogle Scholar
  11. 11.
    Johnson, B.E.: Cohomology in Banach algebras. Mem. Am. Math. Soc. 127 (1972) Google Scholar
  12. 12.
    Johnson, B.E.: Weak amenability of group algebras. Bull. Lond. Math. Soc. 23, 281–284 (1991) MATHCrossRefGoogle Scholar
  13. 13.
    Lau, A.T.-M., Loy, R.J.: Amenability of convolution algebras. Math. Scand. 79, 283–296 (1996) MATHMathSciNetGoogle Scholar
  14. 14.
    Lau, A.T.-M., Zhang, Y.: Fixed point properties of semigroups of non-expansive mappings. J. Funct. Anal. 254, 2534–2554 (2008) MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada

Personalised recommendations