Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-07T23:56:00.961Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak and cyclic amenability for non-commutative Banach algebras

Published online by Cambridge University Press:  20 January 2009

Niels Grønbæk
Niels Grønbæk
Affiliation:
Københavns Universitets Matematiske InstitutUniversitetsparken 5DK-2100 København Ø, Denmark
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.

This paper is concerned with two notions of cohomological triviality for Banach algebras, weak amenability and cyclic amenability. The first is defined within Hochschild cohomology and the latter within cyclic cohomology. Our main result is that where ℱ is a Banach algebraic free product of two Banach algebras and ℬ. It follows that cyclic amenability is preserved under the formation of free products.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 2 , June 1992 , pp. 315 - 328
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Bade, W. G., Curtis, P. C. Jr. and Dales, H. G., Amenability and weak amenability for Beurling and Lipschitz algebras, Proc. London Math. Soc. 57 (1987), 359–377.CrossRefGoogle Scholar
2.Christensen, E., Effros, E. G. and Sinclair, A. M., Completely bounded multilinear maps and C*-algebraic cohomology, Invent. Math. 90 (1987), 279–296.CrossRefGoogle Scholar
3.Connes, A., Non-commutative differential geometry, Inst. Hautes Etudes Sci. Publ. Math. 62 (1985), 41–144.CrossRefGoogle Scholar
4.Feigin, B. L. and Tzyoan, B. L., Additive K-theory, in K-theory, Arithmetic and Geometry (Lecture Notes in Math. 1289, Springer-Verlag, 1987), 67–209.Google Scholar
5.Grønbæk, N., A characterisation of weak amenability, Studia Math. 94 (1989), 149–162.CrossRefGoogle Scholar
6.Haagerup, U., The Grothendieck inequality for bilinear forms on C*-algebras, Adv. in Math. 56(1985), 93–116.CrossRefGoogle Scholar
7.Haagerup, U., All nuclear C*-algebras are amenable, Invent. Math. 74 (1983), 305–319.CrossRefGoogle Scholar
8.Johnson, B. E., Derivations from L1(G) into L1(G) and L∞(G), in Proc. Internal. Conf. on Harmonic Analysis, Luxembourg, 1987 (Lecture Notes in Math., Springer-Verlag), to appear.Google Scholar
9.Johnson, B. E., Weak amenability of group algebras, Preprint, 1990.Google Scholar
10.Sinclair, A. M., Continuous semigrous in Banach algebras, (London Math. Soc. Lecture Notes 63, Cambridge University Press, Cambridge, 1982).CrossRefGoogle Scholar
11.Tzygan, B. L., Homology of matrix Lie algebras over rings and Hochschild homology, Uspekhi Mat. Nauk 38 (1983), 217–218.Google Scholar