Abstract
We establish various results on norm approximations of bounded linear operators acting on the weighted Bergman space \( {\rm A}_\lambda ^2({\mathbb{B}^n}) \) 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 \( {\rm A}_\lambda ^2({\mathbb{B}^n}). \)
Mathematics Subject Classification (2010). Primary 47B35; Secondary 30H20, 30E05.
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Bauer, W., Yañez, C.H., Vasilevski, N. (2014). (m, λ)-Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball. In: Ball, J., Dritschel, M., ter Elst, A., Portal, P., Potapov, D. (eds) Operator Theory in Harmonic and Non-commutative Analysis. Operator Theory: Advances and Applications, vol 240. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-06266-2_3
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DOI: https://doi.org/10.1007/978-3-319-06266-2_3
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-06265-5
Online ISBN: 978-3-319-06266-2
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