ArticleOriginal scientific text

Title

The Berezin transform on the Toeplitz algebra

Authors 1, 2

Affiliations

  1. Department of Mathematics, San Francisco State University, San Francisco, California 94132, U.S.A.
  2. Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240, U.S.A.

Abstract

This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by the analytic Toeplitz operators on the Bergman space.

Bibliography

  1. P. Ahern, M. Flores and W. Rudin, An invariant volume-mean-value property, J. Funct. Anal. 111 (1993), 380-397.
  2. S. Axler, Bergman spaces and their operators, in: Surveys of Some Recent Results in Operator Theory, Vol. 1, J. B. Conway and B. B. Morrel (eds.), Pitman Res. Notes Math., 1988, 1-50.
  3. S. Axler and Ž. Čučković, Commuting Toeplitz operators with harmonic symbols, Integral Equations Operator Theory 14 (1991), 1-12.
  4. S. Axler and P. Gorkin, Algebras on the disk and doubly commuting multiplication operators, Trans. Amer. Math. Soc. 309 (1988), 711-723.
  5. S. Axler and A. Shields, Extensions of analytic and harmonic functions, Pacific J. Math. 145 (1990), 1-15.
  6. S. Axler and D. C. Zheng, Compact operators via the Berezin transform, preprint.
  7. M. Engliš, Functions invariant under the Berezin transform, J. Funct. Anal. 121 (1994), 233-254.
  8. J. B. Garnett, Bounded Analytic Functions, Academic Press, 1981.
  9. K. Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. 86 (1967), 74-111.
  10. S. Kiliç, The Berezin symbol and multipliers of functional Hilbert spaces, Proc. Amer. Math. Soc. 123 (1995), 3687-3691.
  11. G. McDonald and C. Sundberg, Toeplitz operators on the disc, Indiana Univ. Math. J. 28 (1979), 595-611.
  12. K. Stroethoff, Compact Toeplitz operators on Bergman spaces, preprint.
  13. C. Sundberg, Exact sequences for generalized Toeplitz operators, Proc. Amer. Math. Soc. 101 (1987), 634-636.
  14. D. C. Zheng, Hankel operators and Toeplitz operators on the Bergman space, J. Funct. Anal. 83 (1989), 98-120.
Pages:
113-136
Main language of publication
English
Received
1996-10-11
Accepted
1997-07-01
Published
1998
Exact and natural sciences