Amenability of weighted convolution algebras on locally compact groups
Author:
Niels Grønbæk
Journal:
Trans. Amer. Math. Soc. 319 (1990), 765-775
MSC:
Primary 43A20
DOI:
https://doi.org/10.1090/S0002-9947-1990-0962282-5
MathSciNet review:
962282
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Abstract | References | Similar Articles | Additional Information
Abstract: We give a direct transition from the existence of a bounded right approximate identity in the diagonal ideal for a weighted convolution algebra on a locally compact group to the existence of translation invariant means on an associated weighted -space, thus giving a characterization of amenability for such an algebra.
- [1] F. F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, New York 1973. MR 0423029 (54:11013)
- [2] P. C. Curtis, Jr. and R. J. Loy, The structure of amenable Banach algebras, J. London Math. Soc. (to appear).
- [3] F. P. Greenleaf, Invariant means on topological groups, Van Nostrand, New York, 1969. MR 0251549 (40:4776)
- [4] N. Grønbæk, Amenability of weighted discrete convolution algebras on cancellative semi-groups, Proc. Royal Soc. Edinburgh 110A (1988), 351-360.
- [5] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. No. 127 (1972). MR 0374934 (51:11130)
- [6] A. Ya. Khelemskii, Flat Banach modules and amenable algebras, Trans. Moscow Math. Soc. (AMS Transl. 1985) 47 (1984), 199-244. MR 774950 (86g:46108)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1990-0962282-5
Keywords:
Amenable,
bounded approximate identity,
convolution,
diagonal ideal,
translation invariant mean
Article copyright:
© Copyright 1990
American Mathematical Society