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© 2015

Multiplication Operators on the Bergman Space

  • 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

Book

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. Kunyu Guo, Hansong Huang
    Pages 1-6
  3. Kunyu Guo, Hansong Huang
    Pages 7-51
  4. Kunyu Guo, Hansong Huang
    Pages 53-86
  5. Kunyu Guo, Hansong Huang
    Pages 87-123
  6. Kunyu Guo, Hansong Huang
    Pages 125-192
  7. Kunyu Guo, Hansong Huang
    Pages 193-251
  8. Kunyu Guo, Hansong Huang
    Pages 253-268
  9. Kunyu Guo, Hansong Huang
    Pages 269-299
  10. Back Matter
    Pages 301-324

About this book

Introduction

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.

Keywords

46E22,47C15 Bergman space Hilbert space commutant multiplication operators reducing subspaces von Neumann algebra

Authors and affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiChina
  2. 2.Department of MathematicsEast China University of Science and TechnologyShanghaiChina

Bibliographic information

  • Book Title Multiplication Operators on the Bergman Space
  • Authors Kunyu Guo
    Hansong Huang
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • DOI https://doi.org/10.1007/978-3-662-46845-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2015
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-662-46844-9
  • eBook ISBN 978-3-662-46845-6
  • 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
  • Buy this book on publisher's site

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)