Unbounded Weighted Composition Operators in L²-Spaces

Description

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. Front Matter ....Pages i-xii Preliminaries (Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel)....Pages 1-12 Preparatory Concepts (Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel)....Pages 13-32 Subnormality: General Criteria (Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel)....Pages 33-55 C∞-Vectors (Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel)....Pages 57-69 Seminormality (Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel)....Pages 71-92 Discrete Measure Spaces (Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel)....Pages 93-115 Relationships Between Cϕ,w and Cϕ (Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel)....Pages 117-143 Miscellanea (Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel)....Pages 145-160 Back Matter ....Pages 161-182