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Unbounded Weighted Composition Operators in L²-Spaces - Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel

Unbounded Weighted Composition Operators in L²-Spaces

Buch | Softcover
XII, 182 Seiten
2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-74038-6 (ISBN)
CHF 67,35 inkl. MwSt

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.

Chapter 1. Preliminaries.- Chapter 2. Preparatory Concepts.- Chapter 3. Subnormality - General Criteria.- Chapter 4. C -vectors.- Chapter 5. Seminormality.- Chapter 6. Discrete Measure Spaces.- Chapter 7. Relationships Between C ;w and C .- Chapter 8. Miscellanea.

"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)

“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)

Erscheinungsdatum
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo XII, 182 p. 7 illus., 1 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 308 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte conditional expectation • Consistency Condition • hyponormal operator • Moment problems • Normal Operator • Quasinormal Operator • Selfadjoint Operator • Subnormal Operator • tensor product • Weighted Composition Operator
ISBN-10 3-319-74038-5 / 3319740385
ISBN-13 978-3-319-74038-6 / 9783319740386
Zustand Neuware
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