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Unbounded weighted composition operators in L²-Spaces

Author: Piotr Budzyński; Zenon Jan Jablónski; Il Bong Jung; Jan Stochel
Publisher: Cham, Switzerland : Springer, [2018]
Series: Lecture notes in mathematics (Springer-Verlag), 2209.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 weighted composition operators under consideration are not regarded as products of multiplication and composition operators. A variety of seminormality properties are characterized and the first-ever criteria for subnormality of  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
(OCoLC)1016001542
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Piotr Budzyński; Zenon Jan Jablónski; Il Bong Jung; Jan Stochel
ISBN: 9783319740393 3319740393
OCLC Number: 1040652241
Description: 1 online resource (xii, 180 pages) : illustrations
Contents: Chapter 1. Preliminaries --
Chapter 2. Preparatory Concepts --
Chapter 3. Subnormality --
General Criteria --
Chapter 4. C{u221E}-vectors --
Chapter 5. Seminormality --
Chapter 6. Discrete Measure Spaces --
Chapter 7. Relationships Between C{u03D5};w and C{u03D5} --
Chapter 8. Miscellanea.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2209.
Responsibility: by Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel.

Abstract:

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 weighted composition operators under consideration are not regarded as products of multiplication and composition operators. A variety of seminormality properties are characterized and the first-ever criteria for subnormality of unbounded weighted composition operators is provided. The subtle interplay between the classical moment problem, graph theory and the injectivity problem is revealed and there is an investigation of the relationships between weighted composition operators and the corresponding multiplication and composition operators. 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.

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"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 Read more...

 
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