Some Banach algebras without discontinuous derivations

Author:
Brian Forrest

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

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the completion of in either the multiplier norm or the completely bounded multiplier norm is a Banach algebra without discontinuous derivations when is either or .

**[1]**M. Cowling and U. Haagerup,*Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one*, Invent. Math.**96**(1989), 507-549. MR**996553 (90h:22008)****[2]**H. G. Dales and G. Willis,*Cofinite ideals in Banach algebras and finite dimensional representations of group algebras*, Proc. Conf. Automatic Continuity, Lecture Notes in Math., vol. 975, Springer-Verlag, New York, 1982. MR**697603 (84h:46061)****[3]**J. De Canniere and U. Haagerup,*Multipliers of the Fourier algebras of some simple Lie groups and their subgroups*, Amer. J. Math.**107**(1985), 455-500. MR**784292 (86m:43002)****[4]**P. Eymard,*L'algèbre de Fourier d'un groupe localement compact*, Bull. Soc. Math. France**92**(1964), 181-236. MR**0228628 (37:4208)****[5]**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.**[6]**B. Forrest,*Amenability and derivations of the Fourier algebra*, Proc. Amer. Math. Soc.**104**(1988), 437-442. MR**931730 (89c:43001)****[7]**-,*Amenability and bounded approximate identities in ideals of*, Illinois J. Math.**34**(1990), 1-25. MR**1031879 (92e:43003)****[8]**-,*On amenability and some properties of*, preprint.**[9]**E. Hewitt and K. A. Ross,*Abstract harmonic analysis*, vol. 11, Springer-Verlag, New York, 1970. MR**0262773 (41:7378)****[10]**N. P. Jewell,*Continuity of module and higher derivations*, Pacific J. Math.**68**(1977), 91-98. MR**0493341 (58:12369)****[11]**A. T. Lau,*Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups*, Fund. Math.**118**(1983), 161-175. MR**736276 (85k:43007)****[12]**V. Losert,*Properties of the Fourier algebra that are equivalent to amenability*, Proc. Amer. Math. Soc.**91**(1984), 347-354. MR**759651 (86b:43010)****[13]**C. Nebbia,*Multipliers and asymptotic behaviour of the Fourier algebra of nonamenable groups*, Proc. Amer. Math. Soc.**84**(1982), 549-554. MR**643747 (83h:43002)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1068120-4

Keywords:
Fourier algebra,
multipliers,
completely bounded multiplier,
derivation,
free group

Article copyright:
© Copyright 1992
American Mathematical Society