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(m,λ)-Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball

Ball, Joseph A ; Dritschel, Michael A ; ter Elst, A. F. M ; Portal, Pierre ; Potapov, Denis

Operator Theory in Harmonic and Non-Commutative Analysis, 2014, Vol.240, p.45-68 [Periódico revisado por pares]

Switzerland: Springer International Publishing AG

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  • Título:
    (m,λ)-Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball
  • Autor: Ball, Joseph A ; Dritschel, Michael A ; ter Elst, A. F. M ; Portal, Pierre ; Potapov, Denis
  • Assuntos: (m, λ)-Berezin transform ; Functional analysis & transforms ; norm approximation ; Toeplitz operator ; unit ball
  • É parte de: Operator Theory in Harmonic and Non-Commutative Analysis, 2014, Vol.240, p.45-68
  • Notas: Mathematics Subject Classification (2010). Primary 47B35; Secondary 30H20, 30E05.
  • Descrição: We establish various results on norm approximations of bounded linear operators acting on the weighted Bergman space Aλ2(Bn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} {\rm A}_\lambda ^2({\mathbb{B}^n}) \end{document} over the unit ball by means of Toeplitz operators with bounded measurable symbols. The main tool here is the so-called (m, λ)-Berezin transform defined and studied in the paper. In a sense, this is a further development of the ideas and results of [6, 7, 9] to the case of operators acting on Aλ2(Bn).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} {\rm A}_\lambda ^2({\mathbb{B}^n}). \end{document}
  • Títulos relacionados: Operator Theory: Advances and Applications
  • Editor: Switzerland: Springer International Publishing AG
  • Idioma: Inglês

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