Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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
Full-text PDF

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 $ {L^\infty }$-space, thus giving a characterization of amenability for such an algebra.


References [Enhancements On Off] (What's this?)

  • [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)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A20

Retrieve articles in all journals with MSC: 43A20


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

American Mathematical Society