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Weak amenability and the second dual
of the Fourier algebra


Author: Brian Forrest
Journal: Proc. Amer. Math. Soc. 125 (1997), 2373-2378
MSC (1991): Primary 46H20; Secondary 43A20
DOI: https://doi.org/10.1090/S0002-9939-97-03844-6
MathSciNet review: 1389517
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be a locally compact group. We will consider amenability and weak amenability for Banach algebras which are quotients of the second dual of the Fourier algebra. In particular, we will show that if $A(G)^{**}$ is weakly amenable, then $G$ has no infinite abelian subgroup.


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  • 1. R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc., 2 (1951), 839-848. MR 13:659f
  • 2. G. Brown and W. Moran, Point derivations on $M(G)$, Bull. London Math. Soc., 8 (1976), 57-64. MR 54:5744
  • 3. P. Eymard, L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France, 92 (1964), 181-236. MR 37:4208
  • 4. B. Forrest, Arens regularity and the $A_p(G)$ algebras, Proc. Amer. Math. Soc., 119 (1991), 595-598. MR 93k:43003
  • 5. F. Ghahramani, R. J. Loy and G. A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc. 124 (1996), 1489-1497. MR 96g:46036
  • 6. F. Gourdeau, Amenability of Banach algebras, Ph.D. thesis, University of Cambridge, 1989.
  • 7. E. E. Granirer, On some properties of the Banach algebras $A_p(G)$ for locally compact groups, Proc. Amer. Math. Soc., 95 (1985), 375-381. MR 87e:43005
  • 8. -, Density theorems for some linear subspaces and some $C^*$-subalgebras of $VN(G)$, Sympos. Math. INDAM, vol. XXII, Academic Press, New York, 1977, pp. 61-70. MR 58:6935
  • 9. M. L. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math., 53 (1981), 53-73. MR 83b:53041
  • 10. N. Grønbaek, A characterization of weakly amenable Banach algebras, Studia Math., 94 (1989), 149-162. MR 92a:46055
  • 11. B. Johnson, Nonamenability of the Fourier algebra for compact groups, J. London Math. Soc., 50 (1994), 361-374. MR 95i:43001
  • 12. O. Kegel and B. Wehrfritz, Locally Finite Groups, Wiley, New York, 1984. (2nd ed. of MR 57:9848)
  • 13. A. T. Lau, The second conjugate algebra of the Fourier algebra of a locally compact group, Trans. Amer. Math. Soc., 267 (1981), 53-63. MR 83e:43009
  • 14. -, Uniformly continuous functionals on the Fourier algebra of any locally compact group, Trans. Amer. Math. Soc., 251 (1979), 39-59. MR 80m:43009
  • 15. A. T. Lau and V. Losert, The $C^*$-algebra generated by operators with compact support on a locally compact group, J. Funct. Anal., 112 (1993), 1-30. MR 94d:22005
  • 16. A. T. Lau and R. J. Loy, Amenable convolution algebras, preprint.
  • 17. H. Rosenthal, Projections onto translation invariant subspaces of $L^p(G)$, Mem. Amer. Math. Soc. No. 63 (1966). MR 35:2080

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Additional Information

Brian Forrest
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

DOI: https://doi.org/10.1090/S0002-9939-97-03844-6
Keywords: Fourier algebra, second dual, weakly amenable Banach algebra
Received by editor(s): June 5, 1995
Received by editor(s) in revised form: February 26, 1996
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society

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