Unbounded weighted composition operators in L2-spaces / Piotr Budzyński, Zenon Jabłoński, Il Bong Jung... [et al.]

Auteur: Budzyński, Piotr - AuteurCo-auteur: Jabłoński, Zenon (1973-) - Auteur ; Jung, Il Bong (1954-) - Auteur ; Stochel, Jan (1951-) - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 2209Langue: anglaisPays: SwisseÉditeur: Cham : Springer, 2018Description: 1 vol. (xii-180 pages) : fig. ; 24 cm ISBN: 9783319740386 ; br. ISSN: 0075-8434Résumé: Publisher’s description: This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L 2 -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..Bibliographie: Bibliogr. p. 169-174. Index. Sujets MSC: 47-02 Operator theory -- Research exposition (monographs, survey articles)
47B38 Operator theory -- Special classes of linear operators -- Operators on function spaces (general)
47B40 Operator theory -- Special classes of linear operators -- Spectral operators, decomposable operators, well-bounded operators, etc
46E30 Functional analysis -- Linear function spaces and their duals -- Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
42B35 Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Function spaces arising in harmonic analysis
En-ligne: ZbMath | MSN | Springer
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Bibliogr. p. 169-174. Index

Publisher’s description: This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L 2 -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.

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