Weak amenability and the second dual of the Fourier algebra
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- by Brian Forrest PDF
- Proc. Amer. Math. Soc. 125 (1997), 2373-2378 Request permission
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.References
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- Gavin Brown and William Moran, Point derivations on $M(G)$, Bull. London Math. Soc. 8 (1976), no. 1, 57–64. MR 417695, DOI 10.1112/blms/8.1.57
- Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628
- Brian Forrest, Arens regularity and the $A_p(G)$ algebras, Proc. Amer. Math. Soc. 119 (1993), no. 2, 595–598. MR 1169026, DOI 10.1090/S0002-9939-1993-1169026-3
- F. Ghahramani, R. J. Loy, and G. A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc. 124 (1996), no. 5, 1489–1497. MR 1307520, DOI 10.1090/S0002-9939-96-03177-2
- F. Gourdeau, Amenability of Banach algebras, Ph.D. thesis, University of Cambridge, 1989.
- Edmond E. Granirer, On some properties of the Banach algebras $A_p(G)$ for locally compact groups, Proc. Amer. Math. Soc. 95 (1985), no. 3, 375–381. MR 806074, DOI 10.1090/S0002-9939-1985-0806074-X
- Edmond E. Granirer, Density theorems for some linear subspaces and some $C^*$-subalgebras of $\textrm {VN}(G)$, Symposia Mathematica, Vol. XXII (Convegno sull’Analisi Armonica e Spazi di Funzioni su Gruppi Localmente Compatti, INDAM, Rome, 1976) Academic Press, London, 1977, pp. 61–70. MR 0487287
- Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73. MR 623534
- Niels Groenbaek, A characterization of weakly amenable Banach algebras, Studia Math. 94 (1989), no. 2, 149–162. MR 1025743, DOI 10.4064/sm-94-2-149-162
- B. E. Johnson, Non-amenability of the Fourier algebra of a compact group, J. London Math. Soc. (2) 50 (1994), no. 2, 361–374. MR 1291743, DOI 10.1112/jlms/50.2.361
- Otto H. Kegel and Bertram A. F. Wehrfritz, Locally finite groups, North-Holland Mathematical Library, Vol. 3, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973. MR 0470081
- Anthony To Ming Lau, The second conjugate algebra of the Fourier algebra of a locally compact group, Trans. Amer. Math. Soc. 267 (1981), no. 1, 53–63. MR 621972, DOI 10.1090/S0002-9947-1981-0621972-9
- Anthony To Ming Lau, Uniformly continuous functionals on the Fourier algebra of any locally compact group, Trans. Amer. Math. Soc. 251 (1979), 39–59. MR 531968, DOI 10.1090/S0002-9947-1979-0531968-4
- Anthony To Ming Lau and Viktor Losert, The $C^*$-algebra generated by operators with compact support on a locally compact group, J. Funct. Anal. 112 (1993), no. 1, 1–30. MR 1207935, DOI 10.1006/jfan.1993.1024
- A. T. Lau and R. J. Loy, Amenable convolution algebras, preprint.
- Haskell P. Rosenthal, Projections onto translation-invariant subspaces of $L^{p}(G)$, Mem. Amer. Math. Soc. 63 (1966), 84. MR 211198
Additional Information
- Brian Forrest
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
- Received by editor(s): June 5, 1995
- Received by editor(s) in revised form: February 26, 1996
- Communicated by: Theodore W. Gamelin
- © Copyright 1997 American Mathematical Society
- 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