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

Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review

Authors

  • Wolfram Bauer
  • Crispin Herrera Yañez
  • Nikolai Vasilevski

External Research Organisations

  • University of Göttingen
  • Center for Research and Advanced Studies of the National Polytechnic Institute
View graph of relations

Details

Original languageEnglish
Title of host publicationOperator Theory in Harmonic and Non-commutative Analysis
Pages45-68
Number of pages24
Volume240
ISBN (electronic)9783319062662
Publication statusPublished - 30 May 2014
Externally publishedYes

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156

Abstract

We establish various results on norm approximations of bounded linear operators acting on the weighted Bergman space A2λ(Bn) 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 A2λ(Bn).

Keywords

    (m, λ)-berezin transform, Norm approximation, Toeplitz operator, Unit ball

ASJC Scopus subject areas

Cite this

(m, λ)-Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball. / Bauer, Wolfram; Yañez, Crispin Herrera; Vasilevski, Nikolai.
Operator Theory in Harmonic and Non-commutative Analysis. Vol. 240 2014. p. 45-68 (Operator Theory: Advances and Applications).

Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review

Bauer, W, Yañez, CH & Vasilevski, N 2014, (m, λ)-Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball. in Operator Theory in Harmonic and Non-commutative Analysis. vol. 240, Operator Theory: Advances and Applications, pp. 45-68. https://doi.org/10.1007/978-3-319-06266-2_3
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 Operator Theory in Harmonic and Non-commutative Analysis (Vol. 240, pp. 45-68). (Operator Theory: Advances and Applications). https://doi.org/10.1007/978-3-319-06266-2_3
Bauer W, Yañez CH, Vasilevski N. (m, λ)-Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball. In Operator Theory in Harmonic and Non-commutative Analysis. Vol. 240. 2014. p. 45-68. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-319-06266-2_3
Bauer, Wolfram ; Yañez, Crispin Herrera ; Vasilevski, Nikolai. / (m, λ)-Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball. Operator Theory in Harmonic and Non-commutative Analysis. Vol. 240 2014. pp. 45-68 (Operator Theory: Advances and Applications).
Download
@inbook{8721df3d42f44cf28b356b58c1737eb8,
title = "(m, λ)-Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball",
abstract = "We establish various results on norm approximations of bounded linear operators acting on the weighted Bergman space A2λ(Bn) 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 A2λ(Bn).",
keywords = "(m, λ)-berezin transform, Norm approximation, Toeplitz operator, Unit ball",
author = "Wolfram Bauer and Ya{\~n}ez, {Crispin Herrera} and Nikolai Vasilevski",
note = "Publisher Copyright: {\textcopyright} 2014 Springer International Publishing Switzerland. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2014",
month = may,
day = "30",
doi = "10.1007/978-3-319-06266-2_3",
language = "English",
isbn = "9783319062655",
volume = "240",
series = "Operator Theory: Advances and Applications",
pages = "45--68",
booktitle = "Operator Theory in Harmonic and Non-commutative Analysis",

}

Download

TY - CHAP

T1 - (m, λ)-Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball

AU - Bauer, Wolfram

AU - Yañez, Crispin Herrera

AU - Vasilevski, Nikolai

N1 - Publisher Copyright: © 2014 Springer International Publishing Switzerland. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2014/5/30

Y1 - 2014/5/30

N2 - We establish various results on norm approximations of bounded linear operators acting on the weighted Bergman space A2λ(Bn) 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 A2λ(Bn).

AB - We establish various results on norm approximations of bounded linear operators acting on the weighted Bergman space A2λ(Bn) 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 A2λ(Bn).

KW - (m, λ)-berezin transform

KW - Norm approximation

KW - Toeplitz operator

KW - Unit ball

UR - http://www.scopus.com/inward/record.url?scp=84919657392&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-06266-2_3

DO - 10.1007/978-3-319-06266-2_3

M3 - Contribution to book/anthology

AN - SCOPUS:84919657392

SN - 9783319062655

VL - 240

T3 - Operator Theory: Advances and Applications

SP - 45

EP - 68

BT - Operator Theory in Harmonic and Non-commutative Analysis

ER -