Properties of the Fourier algebra that are equivalent to amenability
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- by Viktor Losert PDF
- Proc. Amer. Math. Soc. 92 (1984), 347-354 Request permission
Abstract:
It is shown that a locally compact group $G$ is amenable iff each multiplier on the Fourier algebra $A\left ( G \right )$ is given by a function from the Fourier-Stieltjes algebra $B\left ( G \right )$. Another condition is that the norm of $A\left ( G \right )$ is equivalent to that induced by the regular representation of $A\left ( G \right )$.References
- Larry Baggett, A separable group having a discrete dual space is compact, J. Functional Analysis 10 (1972), 131–148. MR 0346090, DOI 10.1016/0022-1236(72)90045-6
- A. Derighetti, Some results on the Fourier-Stieltjes algebra of a locally compact group, Comment. Math. Helv. 45 (1970), 219–228. MR 412735, DOI 10.1007/BF02567327
- Jean De Cannière and Uffe Haagerup, Multipliers of the Fourier algebras of some simple Lie groups and their discrete subgroups, Amer. J. Math. 107 (1985), no. 2, 455–500. MR 784292, DOI 10.2307/2374423
- Jacques Dixmier, von Neumann algebras, North-Holland Mathematical Library, vol. 27, North-Holland Publishing Co., Amsterdam-New York, 1981. With a preface by E. C. Lance; Translated from the second French edition by F. Jellett. MR 641217 —, ${C^ * }$ -algebras, North-Holland, Amsterdam, 1977.
- Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628
- Hans G. Feichtinger, On a new Segal algebra, Monatsh. Math. 92 (1981), no. 4, 269–289. MR 643206, DOI 10.1007/BF01320058 A. Figà-Talamanca and M. A. Picardello, Multiplicateurs de $A\left ( G \right )$ qui ne sont pas dans $B\left ( G \right )$, C.R. Acad. Sci. Paris Sér. A-B 277 (1973), A117-A119.
- John E. Gilbert, Convolution operators on $L^{p}(G)$ and properties of locally compact groups, Pacific J. Math. 24 (1968), 257–268. MR 231942
- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
- Carl Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 3, 91–123 (English, with French summary). MR 355482
- Carl Herz, Une généralisation de la notion de transformée de Fourier-Stieltjes, Ann. Inst. Fourier (Grenoble) 24 (1974), no. 3, xiii, 145–157 (French, with English summary). MR 425511
- Michael Leinert, A factorable Banach algebra with inequivalent regular representation norm, Proc. Amer. Math. Soc. 60 (1976), 161–162 (1977). MR 420136, DOI 10.1090/S0002-9939-1976-0420136-5
- H. Leptin, On locally compact groups with invariant means, Proc. Amer. Math. Soc. 19 (1968), 489–494. MR 239001, DOI 10.1090/S0002-9939-1968-0239001-7 —, Sur l’algèbre de Fourier d’un groupe localement compact, C.R. Acad. Sci. Paris Sér. A-B 266 (1968), A1180-A1182.
- V. Losert, Some properties of groups without the property $P_{1}$, Comment. Math. Helv. 54 (1979), no. 1, 133–139. MR 522036, DOI 10.1007/BF02566261
- Viktor Losert, A characterization of the minimal strongly character invariant Segal algebra, Ann. Inst. Fourier (Grenoble) 30 (1980), no. 3, 129–139. MR 597020
- Claudio Nebbia, Multipliers and asymptotic behaviour of the Fourier algebra of nonamenable groups, Proc. Amer. Math. Soc. 84 (1982), no. 4, 549–554. MR 643747, DOI 10.1090/S0002-9939-1982-0643747-3
- P. F. Renaud, Centralizers of Fourier algebra of an amenable group, Proc. Amer. Math. Soc. 32 (1972), 539–542. MR 293019, DOI 10.1090/S0002-9939-1972-0293019-8
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 347-354
- MSC: Primary 43A22
- DOI: https://doi.org/10.1090/S0002-9939-1984-0759651-8
- MathSciNet review: 759651