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Multiplication Operators on the Bergman Space

  • Book
  • © 2015

Overview

Authors:
  1. Kunyu Guo

    1. School of Mathematical Sciences, Fudan University, Shanghai, China

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    You can also search for this author in PubMed   Google Scholar

  2. Hansong Huang

    1. Department of Mathematics, East China University of Science and Technology, Shanghai, China

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    You can also search for this author in PubMed   Google Scholar

  • Presents the latest developments on commutants and reducing subspaces of multiplication operators on the Bergman space
  • Reveals von Neumann algebras generated by multiplication operators on the Bergman space
  • Establishes a fascinating connection between operator theory and von Neumann algebra
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2145)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Kunyu Guo, Hansong Huang
    Pages 1-6

  3. Some Preliminaries

    • Kunyu Guo, Hansong Huang
    Pages 7-51

  4. Cowen-Thomson’s Theorem

    • Kunyu Guo, Hansong Huang
    Pages 53-86

  5. Reducing Subspaces Associated with Finite Blaschke Products

    • Kunyu Guo, Hansong Huang
    Pages 87-123

  6. Reducing Subspaces Associated with Thin Blaschke Products

    • Kunyu Guo, Hansong Huang
    Pages 125-192

  7. Covering Maps and von Neumann Algebras

    • Kunyu Guo, Hansong Huang
    Pages 193-251

  8. Similarity and Unitary Equivalence

    • Kunyu Guo, Hansong Huang
    Pages 253-268

  9. Algebraic Structure and Reducing Subspaces

    • Kunyu Guo, Hansong Huang
    Pages 269-299

  10. Back Matter

    Pages 301-324
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Keywords

About this book

This book deals with various aspects of commutants and reducing subspaces of multiplication operators on the Bergman space, along with relevant von Neumann algebras generated by these operators, which have been the focus of considerable attention from the authors and other experts in recent years. The book reviews past developments and offers insights into cutting-edge developments in the study of multiplication operators. It also provides commentary and comparisons to stimulate research in this area.

Reviews

“It is very welcome that the authors have made recent progress in this active area accessible to the community in functional analysis and complex analysis. The reviewer would like to recommend this book strongly to everyone interested in operator theory on Hilbert spaces consisting of holomorphic functions.” (Michio Seto, Mathematical Reviews, August, 2016)

“The book under review, written by two of the main players in the field, is a summary of the developments in the past fifteen years or so about reducing subspaces of multiplication operators on the Bergman space plus a few other closely related topics. The material is well organized, the presentation is smooth, and the mathematics is simply beautiful. I would recommend the book to anyone who is interested in the Bergman space and multiplication operators on it.” (Kehe Zhu, zbMATH 1321.47002, 2015)

Authors and Affiliations

  • School of Mathematical Sciences, Fudan University, Shanghai, China

    Kunyu Guo

  • Department of Mathematics, East China University of Science and Technology, Shanghai, China

    Hansong Huang

Bibliographic Information

  • Book Title: Multiplication Operators on the Bergman Space

  • Authors: Kunyu Guo, Hansong Huang

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-46845-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2015

  • Softcover ISBN: 978-3-662-46844-9Published: 07 July 2015

  • eBook ISBN: 978-3-662-46845-6Published: 23 June 2015

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 322

  • Number of Illustrations: 10 b/w illustrations, 1 illustrations in colour

  • Topics: Operator Theory, Functional Analysis

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