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Abstract:

If μ is a finite measure on the unit disc and k ≥ 0 is an integer, we study a generalization derived from Engliš's work, Tμ(k) m, of the traditional Toeplitz operators on the Bergman space A2, which are the case k = 0. Among other things, we prove that when μ ≥ 0, these operators are bounded if and only if μ is a Carleson measure, they are compact if and only if μ is a vanishing Carleson measure, and we obtain some estimates for their norms. Also, we use these operators to characterize the closure of the image of the Berezin transform applied to the whole operator algebra. © by THETA, 2015.

Registro:

Documento: Artículo
Título:A generalization of Toeplitz operators on the Bergman space
Autor:Suárez, D.
Filiación:Depto. De Matemática, Fac. De Cs. Exactas Y Naturales, Univ. De Buenos Aires, Pab. I, Ciudad Universitaria, (1048), Núñez, Capital Federal, Argentina
Palabras clave:Berezin transform; Bergman space; Toeplitz operators
Año:2015
Volumen:73
Número:2
Página de inicio:315
Página de fin:332
DOI: http://dx.doi.org/10.7900/jot.2013nov28.2023
Título revista:Journal of Operator Theory
Título revista abreviado:J. Oper. Theory
ISSN:03794024
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v73_n2_p315_Suarez

Referencias:

  • Ahern, P., Flores, M., Rudin, W., An invariant volume-mean-value property (1993) J. Funct. Anal., 111, pp. 380-397
  • Berezin, F.A., Covariant and contravariant symbols of operators [Russian] (1972) Izv. Akad. Nauk. USSR Ser. Mat., 6, pp. 1117-1151
  • Berezin, F.A., Quantization in complex symmetric spaces (1975) Izv. Akad. Nauk. USSR Ser. Mat., 9, pp. 341-379
  • Coburn, L.A., A Lipschitz estimate for Berezin's operator calculus (2005) Proc. Amer. Math. Soc., 133, pp. 127-131
  • Engliš, M., Toeplitz operators and group representations (2007) J. Fourier Anal. Appl., 13, pp. 243-265
  • Garnett, J.B., (2007) Bounded Analytic Functions, 236. , Revised first edition, Grad. Texts in Math., Springer, New York
  • Mcdonald, G., Sundberg, C., Toeplitz operators on the disc (1979) Indiana Univ. Math. J., 28, pp. 595-611
  • Rudin, W., (1991) Functional Analysis, , 2nd. edition, McGraw-Hill, New York
  • Stroethoff, K., Zheng, D., Products of Hankel and Toeplitz operators on the Bergman space (1999) J. Funct. Anal., 169, pp. 289-313
  • Suárez, D., Approximation and symbolic calculus for Toeplitz algebras on the Bergman space (2004) Rev. Mat. Iberoamericana, 20, pp. 563-610
  • Suárez, D., Approximation and the n-Berezin transform of operators on the Bergman space (2005) J. Reine Angew. Math., 581, pp. 175-192
  • Suárez, D., The eigenvalues of limits of radial Toeplitz operators (2008) Bull. London Math. Soc., 40, pp. 631-641
  • Zhu, K., (1990) Operator Theory in Function Spaces, , Marcel Dekker Inc., New York

Citas:

---------- APA ----------
(2015) . A generalization of Toeplitz operators on the Bergman space. Journal of Operator Theory, 73(2), 315-332.
http://dx.doi.org/10.7900/jot.2013nov28.2023
---------- CHICAGO ----------
Suárez, D. "A generalization of Toeplitz operators on the Bergman space" . Journal of Operator Theory 73, no. 2 (2015) : 315-332.
http://dx.doi.org/10.7900/jot.2013nov28.2023
---------- MLA ----------
Suárez, D. "A generalization of Toeplitz operators on the Bergman space" . Journal of Operator Theory, vol. 73, no. 2, 2015, pp. 315-332.
http://dx.doi.org/10.7900/jot.2013nov28.2023
---------- VANCOUVER ----------
Suárez, D. A generalization of Toeplitz operators on the Bergman space. J. Oper. Theory. 2015;73(2):315-332.
http://dx.doi.org/10.7900/jot.2013nov28.2023