Abstract
Weak versions of amenability components of BanachL 1(G)-modules are considered. Using these versions, a mean ergodic theorem for locally compact groups is formulated. The possibility of using weak amenability components of operatorL 1(G)-modules to characterize ameable groups is studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. G. Myasnikov, “Amenable BanachL 1(G)-modules, invariant means and regularity in the sense of Arens,”Izv. Vyssh. Uchebn. Zaved. Mat. [Russian Math. (Iz. VUZ)], No. 2, 72–80 (1993).
E. Hewitt and K. A. Ross,Abstract Harmonic Analysis. Vol. 2, Structure and analysis of compact groups. Analysis on locally compact Abelian groups, Springer-Verlag, New York-Berlin (1970).
R. Arens, “The adjoint of a bilinear operation,”Proc. Amer. Math. Soc.,2, 839–848 (1951).
W. R. Emerson, “Characterizations of amenable groups,”Trans. Amer. Math. Soc.,241, 183–194 (1978).
F. P. Greenleaf, “Ergodic theorems and the construction of summing sequences in amenable locally compact groups,”Comm. Pure Appl. Math.,26, 29–46 (1973).
B. Dreseler and W. Schempp, “On the Charshiladze-Lozinski theorem for compact topological groups and homogenous spaces,”Manuscripta Math.,13, 321–337 (1974).
A. L. T. Paterson, “Amenability and translation experiments,”Canad. J. Math.,35, 49–58 (1983).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 879–886, December, 1999.
Rights and permissions
About this article
Cite this article
Myasnikov, A.G. Weak amenability components ofL 1(G)-modules, amenable groups, and an ergodic theorem. Math Notes 66, 726–732 (1999). https://doi.org/10.1007/BF02674330
Issue Date:
DOI: https://doi.org/10.1007/BF02674330