The Berezin transform and operators on spaces of analytic functions
Banach Center Publications (1997)
- Volume: 38, Issue: 1, page 361-380
- ISSN: 0137-6934
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] P. Ahern, M. Flores and W. Rudin, An invariant volume-mean-value property, J. Funct. Anal. 111 (1993), 380-397. Zbl0771.32006
- [2] J. Arazy, S. Fisher and J. Peetre, Hankel operators on weighted Bergman spaces, Amer. J. Math. 110 (1988), 989-1054. Zbl0669.47017
- [3] S. Axler, Bergman spaces and their operators, in: Surveys of Some Recent Results in Operator Theory, Vol. I, J. B. Conway and B. B. % Morrell (eds.), Pitman Res. Notes, 1988, 1-50.
- [4] S. Axler, Berezin symbols and non-compact operators, unpublished manuscript, 1988.
- [5] S. Axler and Ž. Čučković, Commuting Toeplitz operators with harmonic symbols, Integral Equations Operator Theory 14 (1991), 1-12. Zbl0733.47027
- [6] F. A. Berezin, Covariant and contravariant symbols of operators, Math. USSR-Izv. 6 (1972), 1117-1151. Zbl0259.47004
- [7] D. Békollé, C. A. Berger, L. A. Coburn and K. H. Zhu, BMO in the Bergman metric on bounded symmetric domains, J. Funct. Anal. 93 (1990), 310-350. Zbl0765.32005
- [8] C. A. Berger and L. A. Coburn, Toeplitz operators and quantum mechanics, ibid. 68 (1986), 273-299.
- [9] C. A. Berger and L. A. Coburn, Toeplitz operators on the Segal-Bargmann space, Trans. Amer. Math. Soc. 301 (1987), 813-829. Zbl0625.47019
- [10] C. A. Berger, L. A. Coburn and K. H. Zhu, Function theory on Cartan domains and Berezin-Toeplitz symbol calculus, Amer. J. Math. 110 (1988), 921-953. Zbl0657.32001
- [11] A. Brown and P.R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963), 89-102. Zbl0116.32501
- [12] J. A. Cima, K. Stroethoff and K. Yale, Bourgain algebras on the unit disk, Pacific J. Math. 160 (1993), 27-41. Zbl0816.46046
- [13] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. Zbl0469.30024
- [14] V. Guillemin, Toeplitz operators in n-dimensions, Integral Equations Operator Theory 7 (1984), 145-205. Zbl0561.47025
- [15] G.H. Hardy, Divergent Series, Clarendon Press, Oxford, 1949. Zbl0032.05801
- [16] B. Korenblum and K. H. Zhu, An application of Tauberian theorems to Toeplitz operators, J. Operator Theory 33 (1995), 353-361. Zbl0837.47022
- [17] J. Peetre, The Berezin transform and Ha-plitz operators, J. Operator Theory 24 (1990), 165-186. Zbl0793.47026
- [18] P. Rosenthal, Berezin symbols and compactness of operators, unpublished manuscript, 1986.
- [19] W. Rudin, Function Theory in the Unit Ball of , Springer, New York, 1980. Zbl0495.32001
- [20] D. Sarason, personal communication.
- [21] J.H. Shapiro, The essential norm of a composition operator, Ann. of Math. 12 (1987), 375-404. Zbl0642.47027
- [22] K. Stroethoff, Compact Hankel operators on the Bergman space, Illinois J. Math. 34 (1990), 159-174. Zbl0687.47019
- [23] K. Stroethoff, Compact Hankel operators on the Bergman spaces of the unit ball and polydisk in , J. Operator Theory 23 (1990), 153-170. Zbl0723.47018
- [24] K. Stroethoff, Hankel and Toeplitz operators on the Fock space, Michigan Math. J. 39 (1992), 3-16. Zbl0774.47012
- [25] K. Stroethoff, Essentially commuting Toeplitz operators with harmonic symbols, Canad. Math. J. 45 (1993), 1080-1093. Zbl0803.47029
- [26] K. Stroethoff and D. Zheng, Toeplitz and Hankel operators on Bergman spaces, Trans. Amer. Math. Soc. 329 (1992), 773-794. Zbl0755.47020
- [27] K. H. Zhu, VMO, ESV, and Toeplitz operators on the Bergman space, ibid. 302 (1987), 617-646.
- [28] K. H. Zhu, Operator Theory in Function Spaces, Dekker, New York, 1990.