Unbounded Weighted Composition Operators in L²-Spaces
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Beschreibung
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.
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.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
Autor*in
Piotr Budzyński
Themen in »Unbounded Weighted Composition Operators in L²-Spaces«
Weighted Composition Operator Conditional Expectation Hyponormal Operator Subnormal Operator Quasinormal Operator Consistency Condition Moment Problems Tensor Product Selfadjoint Operator Normal Operator
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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 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)
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