m-Berezin transform and compact operators

• Autores: Kyesook Nam, Deyou Zheng, Changyong Zhong
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 22, Nº 3, 2006, págs. 867-892
• Idioma: inglés
• DOI: 10.4171/rmi/477
• Títulos paralelos:
  • Transformada de m-Berezin y operadores compactos
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• Resumen

  • 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 L8 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