m-Berezin transform and compact operators.

Kyesook Nam; Dechao Zheng; Changyong Zhong

Revista Matemática Iberoamericana (2006)

  • Volume: 22, Issue: 3, page 867-892
  • ISSN: 0213-2230

Abstract

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m-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the m-Berezin transform as a linear operator from the space of bounded operators to L∞ is found. We show that the m-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the m-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary of the unit ball.

How to cite

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Nam, Kyesook, Zheng, Dechao, and Zhong, Changyong. "m-Berezin transform and compact operators.." Revista Matemática Iberoamericana 22.3 (2006): 867-892. <http://eudml.org/doc/41996>.

@article{Nam2006,
abstract = {m-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the m-Berezin transform as a linear operator from the space of bounded operators to L∞ is found. We show that the m-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the m-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary of the unit ball.},
author = {Nam, Kyesook, Zheng, Dechao, Zhong, Changyong},
journal = {Revista Matemática Iberoamericana},
keywords = {Espacios de Bergman; Operadores compactos; Transformadas integrales; Operadores de Toeplitz; Integral de Berezin},
language = {eng},
number = {3},
pages = {867-892},
title = {m-Berezin transform and compact operators.},
url = {http://eudml.org/doc/41996},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Nam, Kyesook
AU - Zheng, Dechao
AU - Zhong, Changyong
TI - m-Berezin transform and compact operators.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 3
SP - 867
EP - 892
AB - m-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the m-Berezin transform as a linear operator from the space of bounded operators to L∞ is found. We show that the m-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the m-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary of the unit ball.
LA - eng
KW - Espacios de Bergman; Operadores compactos; Transformadas integrales; Operadores de Toeplitz; Integral de Berezin
UR - http://eudml.org/doc/41996
ER -

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