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

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References

  1. Bateman Manuscript Projct. (Higher Transcendental Functions, Vol. 1). New York-Toronto-London: McGraw-Hill 1953

    Google Scholar 

  2. Borel, A.: Density properties for certain subgroups of semisimple Lie groups without compact factors. Ann. Math.72, 179–188 (1960)

    Google Scholar 

  3. Borel, A., Harish-Chandra, x.: Arithmetic subgroups of algebraic groups. Ann. Math.75, 485–535 (1962)

    Google Scholar 

  4. Bozejko, M.: Positive definite bounded matrices and a characterization of amenable groups. Proc. Am. Math. Soc.95, 357–359 (1985)

    Google Scholar 

  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. Connes, A.: Sur la classification des facteurs de type II. C. R. Acad. Sc. Paris, Sér. A281, 13–15 (1975)

    Google Scholar 

  7. Connes, A., Jones, V.F.R.: PropertyT for von Neumann algebras. Bull. London Math. Soc.17, 57–62 (1985)

    Google Scholar 

  8. Cowling, M.: Unitary and uniformly bounded representations of some simple Lie groups. (Harmonic Analysis and Group Representations, pp. 49–128) Naples: Liguori 1982

    Google Scholar 

  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 1983

    Google Scholar 

  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. 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. Eymard, P.: L'algèbre de Fourier d'un groupe localement compact. Bull. Soc. Math. France92, 181–236 (1964)

    Google Scholar 

  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. Gilbert, J.E.:L p-convolution operators and tensor products of Banach spaces, I, II, III. Preprints, 1973–74

  15. Greenleaf, F.: Invariant means on topological groups. New York: Benjamin 1969

    Google Scholar 

  16. Haagerup, U.: GroupC *-algebras without the completely bounded approximation property. Preprint 1988

  17. Helgason, S.: Differential geometry. (Lie Groups and Symmetric Spaces). New York: Academic Press 1978

    Google Scholar 

  18. Helgason, S.: Groups and geometric analysis. New York: Academic Press 1984

    Google Scholar 

  19. Herz, C.S.: Harmonic synthesis for subgroups. Ann. Inst. Fourier (Grenoble)23, 91–123 (1973)

    Google Scholar 

  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. Kaplan, A.: Riemannian manifolds attached to Clifford modules. Geom. Dedicata11, 127–136 (1981)

    Google Scholar 

  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. Knapp, A.W., Stein, E.M.: Intertwining operators for semisimple groups. Ann. Math.93, 489–578 (1971)

    Google Scholar 

  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. 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. Losert, V.: Properties of the Fourier algebra that are equivalent to amenability. Proc. Am. Math. Soc.92, 347–354 (1984)

    Google Scholar 

  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. 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. Prasad, G.: Strong rigidity inQ-rank 1 lattices. Invent. Math.21, 255–286 (1973)

    Google Scholar 

  30. Sakai, S.:C *-algebras andW *-algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 60). Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  31. Titchmarsh, E.C.: The theory of functions. Oxford: Oxford Univ. Press 1978

    Google Scholar 

  32. Umegaki, H.: Conditional expectation in an operator algebra. Tôhoku Math. J.6, 177–181 (54)

    Google Scholar 

  33. Zimmer, R.J.: Ergodic theory and semisimple groups. (Monographs in Mathematics, Vol. 81). Boston-Basel-Stuttgart: Birkhäuser 1984

    Google Scholar 

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Cowling, M., Haagerup, U. Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one. Invent Math 96, 507–549 (1989). https://doi.org/10.1007/BF01393695

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