Annali di Matematica Pura ed Applicata

, Volume 172, Issue 1, pp 379–394 | Cite as

Schatten class composition operators on weighted Bergman spaces of bounded symmetric domains

  • Song-Ying Li
  • Bernard Russo


We obtain trace ideal criteria for 0<p<∞ for holomorphic composition operators acting on the weighted Bergman spacesA α 2 (Ω) of a Bounded symmetric diomain Ω in ℂn.


Composition Operator Bergman Space Symmetric Domain Class Composition Ideal Criterion 
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  1. [1]
    F. Beatrous -S.-Y. Li,Trace ideal criteria for operators of Hankel type, Ill. J. Math.,39 (1995), pp. 723–754.Google Scholar
  2. [2]
    D. Békollé -C. A. Berger -L. A. Coburn -K. Zhu,BMO in the Bergman metric on bounded symmetric domains, J. Funct. Anal.,93 (1990), pp. 310–350.Google Scholar
  3. [3]
    D. Békollé -A. Bonami,Estimates for the Bergman and Szegö projections in two symmetric domains of ℂ n, Colloq. Math.,68 (1995), pp. 81–100.Google Scholar
  4. [4]
    C. A. Berger -L. A. Coburn -K. Zhu,Function theory on Cartan domains and the Berezin-Toeplitz calculus, Amer. J. Math.,110 (1988), pp. 921–953.Google Scholar
  5. [5]
    A. Cima -W. Wogen,Unbounded composition operators on H 2(B n), Proc. Amer. Math. Soc.,99 (1987), pp. 477–483.Google Scholar
  6. [6]
    R, Coifman -R. Rochberg,Representation theorems for holomorphic and harmonic functions in L p, Astérique,77 (1980), pp. 11–66.Google Scholar
  7. [7]
    C. C.Cowen,Composition operators on Hilbert spaces of analytic functions; A status report, in:Proc. Sympos. Pure Math. (W. B. Arveson - R. G. Douglas, Eds.),51 (1990), pp. 131–145.Google Scholar
  8. [8]
    J. Faraut -A. Koranyi,Function spaces and reproducing kernels on bounded symmetric domains, J. Funct. Anal.,88 (1990), pp. 64–89.Google Scholar
  9. [9]
    P. Jafari,Composition operators in Bergman spaces on bounded symmetric domains, Contemp. Math.,137 (1992), pp. 277–290.Google Scholar
  10. [10]
    S. G.Krantz,Function Theory of Several Complex Variables, Wadsworth & Brooks, 2nd edition (1992).Google Scholar
  11. [11]
    S.-Y. Li,Trace ideal criteria for composition operators on Bergman spaces, Amer. J. Math.,117 (1995), pp. 1299–1323.Google Scholar
  12. [12]
    S.-Y. Li -B. Russo,On compactness of composition operators in Hardy spaces of several variables, Proc Amer. Math. Soc.,123 (1995), pp. 161–171.Google Scholar
  13. [13]
    D. H. Luecking,Trace ideal criteria for Toeplitz operators, J. Funct. Anal.,73 (1987), pp. 345–368.Google Scholar
  14. [14]
    D. Luecking -K. Zhu,Composition operators belonging to the Scatten ideals, Amer. J. Math.,114 (1992), pp. 1127–1145.Google Scholar
  15. [15]
    B. Maccluer,Spectra of compact composition operators on H p(B N), Analysis,4 (1984), pp. 87–103.Google Scholar
  16. [16]
    B. Maccluer -J. H. Shapiro,Angular derivatives and compact composition operators on Hardy and Bergman spaces, Can. J. Math.,38 (1986), pp. 878–906.Google Scholar
  17. [17]
    M. M. Peloso,Hankel operators on weighted Bergman spaces on strongly pseudoconvex domains, Ill. J. Math.,38 (1994), pp. 223–249.Google Scholar
  18. [18]
    J. H. Shapiro,The essential norm of a composition operator, Ann. Math.,125 (1987), pp. 375–404.Google Scholar
  19. [19]
    J. H. Shapiro -P. D. Taylor,Compact nuclear and Hilbert-Schmidt composition operators on H 2, Indiana Univ. Math. J.,23 (1973), pp. 471–496.Google Scholar
  20. [20]
    W.Wogen,Composition operators acting on spaces of holomorphic functions on domains in ℂn, in:Proc. Sympos. Pure Math. (W. B. Arveson - R. G. Douglas, Eds.),51 (1990), pp. 361–366.Google Scholar
  21. [21]
    K. Zhu,Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains, J. Operator Theory,20 (1988), pp. 329–357.Google Scholar
  22. [22]
    K. Zhu,Operator Theory in Function Spaces, M. Dekker, New York (1990).Google Scholar

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© Fondazione Annali di Matematica Pura ed Applicata 1997

Authors and Affiliations

  • Song-Ying Li
    • 1
  • Bernard Russo
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.Department of MathematicsUniversity of CaliforniaIrvineUSA

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