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Unbounded Weighted Composition Operators in L²-Spaces

  • Book
  • © 2018

Overview

Authors:
  1. Piotr Budzyński

    1. Katedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, Kraków, Poland

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  2. Zenon Jabłoński

    1. Instytut Matematyki, Uniwersytet Jagielloński, Kraków, Poland

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  3. Il Bong Jung

    1. Department of Mathematics, Kyungpook National University, Daegu, Korea (Republic of)

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  4. Jan Stochel

    1. Instytut Matematyki, Uniwersytet Jagielloński, Kraków, Poland

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  • Provides the first systematic study of unbounded weighted composition operators in L² spaces in full generality
  • Contains the first ever criteria for subnormality of unbounded weighted composition operators in L² -spaces
  • Includes a detailed discussion of some basic properties of conditional expectation in non-probabilistic setting

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2209)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Preliminaries

    • Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel
    Pages 1-12

  3. Preparatory Concepts

    • Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel
    Pages 13-32

  4. Subnormality: General Criteria

    • Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel
    Pages 33-55

  5. C ∞-Vectors

    • Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel
    Pages 57-69

  6. Seminormality

    • Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel
    Pages 71-92

  7. Discrete Measure Spaces

    • Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel
    Pages 93-115

  8. Relationships Between Cϕ,w and C ϕ

    • Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel
    Pages 117-143

  9. Miscellanea

    • Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel
    Pages 145-160

  10. Back Matter

    Pages 161-182
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Keywords

About this book

This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L²-spaces. It develops the theory in full generality, meaning that the corresponding composition operators are not assumed to be well defined. A variety of seminormality properties of unbounded weighted composition operators are characterized.

The first-ever criteria for subnormality of unbounded weighted composition operators are provided and the subtle interplay between the classical moment problem, graph theory and the injectivity problem for weighted composition operators is revealed. The relationships between weighted composition operators and the corresponding multiplication and composition operators are investigated. The optimality of the obtained results is illustrated by a variety of examples, including those of discrete and continuous types.

The book is primarily aimed at researchers in single or multivariable operator theory.

Reviews

“All in all, the book under review presents a rigorous measure-theoretic development of the theory of bounded and unbounded WCOs in L2-measure spaces. … The book can serve as a comprehensive resource for researchers in operator theory, in particular WCO/CO researchers, and those interested in measure theory, dynamical systems, graph theory, as well as multidisciplinary researchers working in these areas and their applications.” (Abebaw Tadesse, Mathematical Reviews, March, 2019)​

Authors and Affiliations

  • Katedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, Kraków, Poland

    Piotr Budzyński

  • Instytut Matematyki, Uniwersytet Jagielloński, Kraków, Poland

    Zenon Jabłoński, Jan Stochel

  • Department of Mathematics, Kyungpook National University, Daegu, Korea (Republic of)

    Il Bong Jung

Bibliographic Information

  • Book Title: Unbounded Weighted Composition Operators in L²-Spaces

  • Authors: Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-74039-3

  • Publisher: Springer Cham

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

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Softcover ISBN: 978-3-319-74038-6Published: 29 May 2018

  • eBook ISBN: 978-3-319-74039-3Published: 28 May 2018

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 182

  • Number of Illustrations: 6 b/w illustrations, 1 illustrations in colour

  • Topics: Operator Theory, Functional Analysis, Measure and Integration

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