Some Banach algebras without discontinuous derivations
HTML articles powered by AMS MathViewer
- by Brian Forrest PDF
- Proc. Amer. Math. Soc. 114 (1992), 965-970 Request permission
Abstract:
It is shown that the completion of $A(G)$ in either the multiplier norm or the completely bounded multiplier norm is a Banach algebra without discontinuous derivations when $G$ is either ${F_2}$ or $\operatorname {SL}(2,\mathbb {R})$.References
- Michael Cowling and Uffe Haagerup, Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one, Invent. Math. 96 (1989), no. 3, 507–549. MR 996553, DOI 10.1007/BF01393695
- H. G. Dales and G. A. Willis, Cofinite ideals in Banach algebras, and finite-dimensional representations of group algebras, Radical Banach algebras and automatic continuity (Long Beach, Calif., 1981), Lecture Notes in Math., vol. 975, Springer, Berlin-New York, 1983, pp. 397–407. MR 697603
- 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
- Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628 A. Figa-Talamenca, A remark on multipliers of the Fourier algebra of the free group, Boll. Un. Mat. Ital, A (6) 16 (1979), 571-581.
- Brian Forrest, Amenability and derivations of the Fourier algebra, Proc. Amer. Math. Soc. 104 (1988), no. 2, 437–442. MR 931730, DOI 10.1090/S0002-9939-1988-0931730-5
- Brian Forrest, Amenability and bounded approximate identities in ideals of $A(G)$, Illinois J. Math. 34 (1990), no. 1, 1–25. MR 1031879 —, On amenability and some properties of $\operatorname {Ap}(G)$, preprint.
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773
- Nicholas P. Jewell, Continuity of module and higher derivations, Pacific J. Math. 68 (1977), no. 1, 91–98. MR 493341
- Anthony To Ming Lau, Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups, Fund. Math. 118 (1983), no. 3, 161–175. MR 736276, DOI 10.4064/fm-118-3-161-175
- Viktor Losert, Properties of the Fourier algebra that are equivalent to amenability, Proc. Amer. Math. Soc. 92 (1984), no. 3, 347–354. MR 759651, DOI 10.1090/S0002-9939-1984-0759651-8
- 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
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 965-970
- MSC: Primary 43A07; Secondary 43A15, 46J10
- DOI: https://doi.org/10.1090/S0002-9939-1992-1068120-4
- MathSciNet review: 1068120