Inventiones mathematicae

, Volume 96, Issue 3, pp 507–549 | Cite as

Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one

  • Michael Cowling
  • Uffe Haagerup


Fourier Real Rank Fourier Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bateman Manuscript Projct. (Higher Transcendental Functions, Vol. 1). New York-Toronto-London: McGraw-Hill 1953Google Scholar
  2. 2.
    Borel, A.: Density properties for certain subgroups of semisimple Lie groups without compact factors. Ann. Math.72, 179–188 (1960)Google Scholar
  3. 3.
    Borel, A., Harish-Chandra, x.: Arithmetic subgroups of algebraic groups. Ann. Math.75, 485–535 (1962)Google Scholar
  4. 4.
    Bozejko, M.: Positive definite bounded matrices and a characterization of amenable groups. Proc. Am. Math. Soc.95, 357–359 (1985)Google Scholar
  5. 5.
    Bozejko, M., Fendler, G.: Herz-Schur multipliers and completely bounded multipliers of the Fourier algebra of a locally compact group. Boll. Unione Mat. Ital., V. Ser., A3, 297–302 (1984)Google Scholar
  6. 6.
    Connes, A.: Sur la classification des facteurs de type II. C. R. Acad. Sc. Paris, Sér. A281, 13–15 (1975)Google Scholar
  7. 7.
    Connes, A., Jones, V.F.R.: PropertyT for von Neumann algebras. Bull. London Math. Soc.17, 57–62 (1985)Google Scholar
  8. 8.
    Cowling, M.: Unitary and uniformly bounded representations of some simple Lie groups. (Harmonic Analysis and Group Representations, pp. 49–128) Naples: Liguori 1982Google Scholar
  9. 9.
    Cowling, M.: Harmonic analysis on some nilpotent groups (with applications to the representation theory of some semisimple Lie groups). (Topics in Modern Harmonic Analysis, Vol. I, pp. 81–123). Istituto Nazionale di Alta Matematica, Roma 1983Google Scholar
  10. 10.
    Cowling, M., Korányi, A.: Harmonic analysis on Heisenberg type groups from a geometric viewpoint, in Lie Group Representations III. (Lecture Notes in Math., Vol. 1077. Berlin-Heidelberg-New York: Springer 1984)Google Scholar
  11. 11.
    De Cannière, J., Haagerup, U.: Multipliers of the Fourier algebra of some simple Lie groups and their discrete subgroups. Am. J. Math.107, 455–500 (1984)Google Scholar
  12. 12.
    Eymard, P.: L'algèbre de Fourier d'un groupe localement compact. Bull. Soc. Math. France92, 181–236 (1964)Google Scholar
  13. 13.
    Geller, D., Stein, E.M.: Singular convolution operators on the Heisenberg group. Bull. Am. Math. Soc., New Ser.6, 99–103 (1982)Google Scholar
  14. 14.
    Gilbert, J.E.:L p-convolution operators and tensor products of Banach spaces, I, II, III. Preprints, 1973–74Google Scholar
  15. 15.
    Greenleaf, F.: Invariant means on topological groups. New York: Benjamin 1969Google Scholar
  16. 16.
    Haagerup, U.: GroupC *-algebras without the completely bounded approximation property. Preprint 1988Google Scholar
  17. 17.
    Helgason, S.: Differential geometry. (Lie Groups and Symmetric Spaces). New York: Academic Press 1978Google Scholar
  18. 18.
    Helgason, S.: Groups and geometric analysis. New York: Academic Press 1984Google Scholar
  19. 19.
    Herz, C.S.: Harmonic synthesis for subgroups. Ann. Inst. Fourier (Grenoble)23, 91–123 (1973)Google Scholar
  20. 20.
    Herz, C.S.: Une généralisation de la notion de transformée de Fourier-Stieltjes. Ann. Inst. Fourier (Grenoble)24, 145–157 (1974)Google Scholar
  21. 21.
    Kaplan, A.: Riemannian manifolds attached to Clifford modules. Geom. Dedicata11, 127–136 (1981)Google Scholar
  22. 22.
    Kazhdan, D.A.: Connection of the dual space of a group with the structure of its closed subgroups. Funct. Anal. Appl.1, 63–65 (1967)Google Scholar
  23. 23.
    Knapp, A.W., Stein, E.M.: Intertwining operators for semisimple groups. Ann. Math.93, 489–578 (1971)Google Scholar
  24. 24.
    Kostant, B.: On the existence and irreducibility of a certain series of representations. Bull. Am. Math. Soc.75, 627–642 (1969)Google Scholar
  25. 25.
    Leptin, H.: Sur l'algèbre de Fourier d'un groupe localement compact. C. R. Acad. Sc. Paris, Sér. A266, 1180–1182 (1968)Google Scholar
  26. 26.
    Losert, V.: Properties of the Fourier algebra that are equivalent to amenability. Proc. Am. Math. Soc.92, 347–354 (1984)Google Scholar
  27. 27.
    Nakamura, M., Takesaki, M., Umegaki, H.: A remark on expectations of operator algebras. Kodai Math. Sem. Rep.12, 82–90 (1960)Google Scholar
  28. 28.
    Nebbia, C.: Multipliers and asymptotic behaviour of the Fourier algebra of non amenable groups. Proc. Am. Math. Soc.84, 549–554 (1982)Google Scholar
  29. 29.
    Prasad, G.: Strong rigidity inQ-rank 1 lattices. Invent. Math.21, 255–286 (1973)Google Scholar
  30. 30.
    Sakai, S.:C *-algebras andW *-algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 60). Berlin-Heidelberg-New York: Springer 1971Google Scholar
  31. 31.
    Titchmarsh, E.C.: The theory of functions. Oxford: Oxford Univ. Press 1978Google Scholar
  32. 32.
    Umegaki, H.: Conditional expectation in an operator algebra. Tôhoku Math. J.6, 177–181 (54)Google Scholar
  33. 33.
    Zimmer, R.J.: Ergodic theory and semisimple groups. (Monographs in Mathematics, Vol. 81). Boston-Basel-Stuttgart: Birkhäuser 1984Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Michael Cowling
    • 1
  • Uffe Haagerup
    • 2
  1. 1.School of MathematicsUniversity of New South WalesKensingtonAustralia
  2. 2.Matematisk InstitutOdense UniversitetOdense-MDenmark

Personalised recommendations