The Berezin transform on the Toeplitz algebra

Sheldon Axler; Dechao Zheng

Studia Mathematica (1998)

  • Volume: 127, Issue: 2, page 113-136
  • ISSN: 0039-3223

Abstract

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

How to cite

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Axler, Sheldon, and Zheng, Dechao. "The Berezin transform on the Toeplitz algebra." Studia Mathematica 127.2 (1998): 113-136. <http://eudml.org/doc/216463>.

@article{Axler1998,
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.},
author = {Axler, Sheldon, Zheng, Dechao},
journal = {Studia Mathematica},
keywords = {Toeplitz algebra; Berezin transform; Bergman space},
language = {eng},
number = {2},
pages = {113-136},
title = {The Berezin transform on the Toeplitz algebra},
url = {http://eudml.org/doc/216463},
volume = {127},
year = {1998},
}

TY - JOUR
AU - Axler, Sheldon
AU - Zheng, Dechao
TI - The Berezin transform on the Toeplitz algebra
JO - Studia Mathematica
PY - 1998
VL - 127
IS - 2
SP - 113
EP - 136
AB - This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by the analytic Toeplitz operators on the Bergman space.
LA - eng
KW - Toeplitz algebra; Berezin transform; Bergman space
UR - http://eudml.org/doc/216463
ER -

References

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  2. [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. [3] S. Axler and Ž. Čučković, Commuting Toeplitz operators with harmonic symbols, Integral Equations Operator Theory 14 (1991), 1-12. Zbl0733.47027
  4. [4] S. Axler and P. Gorkin, Algebras on the disk and doubly commuting multiplication operators, Trans. Amer. Math. Soc. 309 (1988), 711-723. Zbl0706.46040
  5. [5] S. Axler and A. Shields, Extensions of analytic and harmonic functions, Pacific J. Math. 145 (1990), 1-15. Zbl0732.30026
  6. [6] S. Axler and D. C. Zheng, Compact operators via the Berezin transform, preprint. Zbl0914.47029
  7. [7] M. Engliš, Functions invariant under the Berezin transform, J. Funct. Anal. 121 (1994), 233-254. Zbl0807.47017
  8. [8] J. B. Garnett, Bounded Analytic Functions, Academic Press, 1981. Zbl0469.30024
  9. [9] K. Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. 86 (1967), 74-111. Zbl0192.48302
  10. [10] S. Kiliç, The Berezin symbol and multipliers of functional Hilbert spaces, Proc. Amer. Math. Soc. 123 (1995), 3687-3691. Zbl0847.46010
  11. [11] G. McDonald and C. Sundberg, Toeplitz operators on the disc, Indiana Univ. Math. J. 28 (1979), 595-611. Zbl0439.47022
  12. [12] K. Stroethoff, Compact Toeplitz operators on Bergman spaces, preprint. 
  13. [13] C. Sundberg, Exact sequences for generalized Toeplitz operators, Proc. Amer. Math. Soc. 101 (1987), 634-636. Zbl0642.47012
  14. [14] D. C. Zheng, Hankel operators and Toeplitz operators on the Bergman space, J. Funct. Anal. 83 (1989), 98-120. Zbl0678.47026

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