Semi-amenability and Connes Semi-amenability of Banach Algebras

Authors

1 Department of Mathematics Science and Research Branch, Islamic Azad University, Tehran of Iran.

2 Department of Mathematics, University of Mohaghegh Ardabili, Ardabil of Iran.

Abstract

Let A be a Banach algebra and X a Banach A-bimodule, the derivation D : A → X is semi-inner if there are ξ, μ ∈ X such that D(a) = a.ξ − μ.a, (a ∈ A). A is called semi-amenable if every derivation D : A → X∗ is semi-inner. The dual Banach algebra A is Connes semi-amenable (resp. approximately semi-amenable) if, every D ∈ Z1w _ (A,X), for each normal, dual Banach A-bimodule X, is semi -inner (resp. approximately semi-inner). We will investigate on some properties of semi-amenability and Connes semiamenability of Banach algebras which former have been studied for amenability case.

Keywords

References

1. W.G. Bade, P.C. Curtis and H.G. Dales, Amenability and weak amenability for Beurling and Lipschitz algebra, Proc. London Math. Soc., 3(55), 359–377 (1999).
2. H.G. Dales, Banach Algebra and Automatic Continuity, Oxford, (2000).
3. F. Ghahramani, R.J. Loy, Approximate amenability of tensor products of Banach algebras, J. Math. Anal. Appl., 454(2), 1–16 (2017).
4. F. Ghahramani, R.J. Loy, Generalized notions of amenability, J. Funct. Anal., 208, 229–260 (2004).
5. F. Ghahramani, R.J. Loy, Y. Zhang, Generalized notions of amenability, II, J. Funct. Anal., 254 (7), 1776–1810 (2008).
6. A. Ya. Helemskii, Homological essence of amenability in the sence of A. Connes: the injectivity of the predual bimodule (translated from the Russian), Math. USSR-Sb, 68, 555–566 (1991).
7. B.E. Johnson, Cohomology in Banach algebra, Mem. Amer. Math. Soc., 127, (1972).
8. B.E. Johnson, Derivation from L1(G) into L1(G) and L1(G), Lecture Notes in Math., 1359, Springer, Berlin, 191–198 (1988).
9. B.E. Johnson, R.V. Kadison and J. Ringrose, Cohomology of operator algebras, III, Bull. Soc. Math. France, 100, 73–79 (1972).
10. V. Runde, Amenability for dual Banach algebras, Studia Math., 148, 47–66 (2001).
11. V. Runde, Lectures on the Amenability, Springer-Verlag Berlin Heideberg, New York (2002).
 
Global Analysis and Discrete Mathematics
Volume 3, Issue 1
November 2018
Pages 53-63

Files

History

  • Receive Date: 19 November 2018
  • Accept Date: 19 November 2018

Share

How to cite

Statistics