Czechoslovak Mathematical Journal

, Volume 55, Issue 4, pp 863–876 | Cite as

Problems Concerning n-Weak Amenability of a Banach Algebra

  • Alireza Medghalchi
  • Taher Yazdanpanah


In this paper we extend the notion of n-weak amenability of a Banach algebra \(A\) when n ∈ ℕ. Technical calculations show that when \(A\) is Arens regular or an ideal in \(A\)**, then \(A\)* is an \(A\)(2n)-module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of n-weak amenability to n ∈ ∕.


Banach algebra weakly amenable Arens regular n-weakly amenable 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    W. G. Bade, P. G. Curtis and H. G. Dales: Amenability and weak amenability for Beurling and Lipschitz algebra. Proc. London Math. Soc. 55 (1987), 359–377.MathSciNetGoogle Scholar
  2. [2]
    H. G. Dales, F. Ghahramanim and N. Gronbaek: Derivations into iterated duals of Banach algebras. Studia Math. 128 (1998), 19–54.MathSciNetGoogle Scholar
  3. [3]
    H. G. Dales, A. Rodriguez-Palacios and M. V. Valasco: The second transpose of a derivation. J. London Math. Soc. 64 (2001), 707–721.MathSciNetGoogle Scholar
  4. [4]
    M. Despic and F. Ghahramani: Weak amenability of group algebras of locally compact groups. Canad. Math. Bull. 37 (1994), 165–167.MathSciNetGoogle Scholar
  5. [5]
    J. Duncan and Hosseiniun: The second dual of a Banach algebra. Proc. Roy. Soc. Edinburgh 84A (1978), 309–325.MathSciNetGoogle Scholar
  6. [6]
    N. Gronbaek: Weak amenability of group algebras. Bull. London Math. Soc. 23 (1991), 231–284.Google Scholar
  7. [7]
    U. Haagerup: All nuclear \(C\)*-algebras are amenable. Invent. Math. 74 (1983), 305–319.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    B. E. Johnson: Cohomology in Banach Algebras. Mem. Amer. Math. Soc. 127 (1972).Google Scholar
  9. [9]
    B. E. Johnson: Weak amenability of group algebras. Bull. Lodon Math. Soc. 23 (1991), 281–284.MATHGoogle Scholar
  10. [10]
    T. W. Palmer: Banach Algebra, the General Theory of *-algebra. Vol. 1: Algebra and Banach Algebras. Cambridge University Press, Cambridge, 1994.Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2005

Authors and Affiliations

  • Alireza Medghalchi
    • 1
  • Taher Yazdanpanah
    • 2
  1. 1.Faculty of Mathematical ScienceTeacher Training UniversityTehranIran
  2. 2.Department of MathematicsPersian Gulf UniversityBoushehrIran

Personalised recommendations