Unbounded Weighted Composition Operators In L2 Spaces

Author : Piotr Budzyński,Zenon Jabłoński,Il Bong Jung,Jan Stochel
Publisher : Springer
Page : 182 pages
File Size : 46,9 Mb
Release : 2018-05-28
Category : Mathematics
ISBN : 9783319740393

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

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.

Author : R.K. Singh,J.S. Manhas
Publisher : Elsevier
Page : 314 pages
File Size : 53,8 Mb
Release : 1993-11-03
Category : Mathematics
ISBN : 0080872905

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Composition Operators on Function Spaces by R.K. Singh,J.S. Manhas Pdf

This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics. After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed. This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers.

Author : Farhad Jafari,Rocky Mountain Mathematics Consortium
Publisher : American Mathematical Soc.
Page : 252 pages
File Size : 40,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821807682

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Studies on Composition Operators by Farhad Jafari,Rocky Mountain Mathematics Consortium Pdf

This book reflects the proceedings of the 1996 Rocky Mountain Mathematics Consortium conference on ``Composition Operators on Spaces of Analytic Functions'' held at the University of Wyoming. The readers will find here a collection of high-quality research and expository articles on composition operators in one and several variables. The book highlights open questions and new advances in the classical areas and promotes topics which are left largely untreated in the existing texts. In the past two decades, the study of composition operators has experienced tremendous growth. Many connections between the study of these operators on various function spaces and other branches of analysis have been established. Advances in establishing criteria for membership in different operator classes have led to progress in the study of the spectra, adjoints, and iterates of these operators. More recently, connections between these operators and the study of the invariant subspace problem, functional equations, and dynamical systems have been exploited.

Author : Carl C. Cowen, Jr.,Barbara I. MacCluer
Publisher : Routledge
Page : 401 pages
File Size : 45,6 Mb
Release : 2019-03-04
Category : Mathematics
ISBN : 9781351459143

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Composition Operators on Spaces of Analytic Functions by Carl C. Cowen, Jr.,Barbara I. MacCluer Pdf

The study of composition operators lies at the interface of analytic function theory and operator theory. Composition Operators on Spaces of Analytic Functions synthesizes the achievements of the past 25 years and brings into focus the broad outlines of the developing theory. It provides a comprehensive introduction to the linear operators of composition with a fixed function acting on a space of analytic functions. This new book both highlights the unifying ideas behind the major theorems and contrasts the differences between results for related spaces. Nine chapters introduce the main analytic techniques needed, Carleson measure and other integral estimates, linear fractional models, and kernel function techniques, and demonstrate their application to problems of boundedness, compactness, spectra, normality, and so on, of composition operators. Intended as a graduate-level textbook, the prerequisites are minimal. Numerous exercises illustrate and extend the theory. For students and non-students alike, the exercises are an integral part of the book. By including the theory for both one and several variables, historical notes, and a comprehensive bibliography, the book leaves the reader well grounded for future research on composition operators and related areas in operator or function theory.

Author : Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar
Publisher : Springer Nature
Page : 893 pages
File Size : 44,6 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9783031505355

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Multivariable Operator Theory by Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar Pdf

Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Author : Zenon Jan Jablónski,Il Bong Jung,Jan Stochel
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 40,5 Mb
Release : 2012
Category : Linear operators
ISBN : 9780821868683

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Weighted Shifts on Directed Trees by Zenon Jan Jablónski,Il Bong Jung,Jan Stochel Pdf

A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and of weighted adjacency operators, on the other; they are called weighted shifts on directed trees. The basic properties of such operators, including closedness, adjoints, polar decomposition and moduli are studied. Circularity and the Fredholmness of weighted shifts on directed trees are discussed. The relationships between domains of a weighted shift on a directed tree and its adjoint are described. Hyponormality, cohyponormality, subnormality and complete hyperexpansivity of such operators are entirely characterized in terms of their weights. Related questions that arose during the study of the topic are solved as well.

Author : Seymour Goldberg
Publisher : Unknown
Page : 216 pages
File Size : 42,8 Mb
Release : 1966
Category : Algebras, Linear
ISBN : UCAL:B4407348

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Unbounded Linear Operators by Seymour Goldberg Pdf

Author : B. Grigelionis,J. Kubilius,H. Pragarauskas,V. Statulevičius
Publisher : Walter de Gruyter GmbH & Co KG
Page : 752 pages
File Size : 48,8 Mb
Release : 2020-05-18
Category : Mathematics
ISBN : 9783112319321

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Probability Theory and Mathematical Statistics by B. Grigelionis,J. Kubilius,H. Pragarauskas,V. Statulevičius Pdf

No detailed description available for "Probability Theory and Mathematical Statistics".

Author : Joseph A. Ball,Yuli Eidelman,J. William Helton,Vadim Olshevsky,James Rovnyak
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 54,7 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9783764385392

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Recent Advances in Matrix and Operator Theory by Joseph A. Ball,Yuli Eidelman,J. William Helton,Vadim Olshevsky,James Rovnyak Pdf

This volume comprises the proceedings of the International Workshop on Operator Theory and Its Applications held at the University of Connecticut in July 2005.

Author : Kehe Zhu
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 45,8 Mb
Release : 2007
Category : Function spaces
ISBN : 9780821839652

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Operator Theory in Function Spaces by Kehe Zhu Pdf

This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.

Author : Anonim
Publisher : Unknown
Page : 932 pages
File Size : 42,9 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015078588798

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Mathematical Reviews by Anonim Pdf

Author : Kehe Zhu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 47,7 Mb
Release : 2012-05-26
Category : Mathematics
ISBN : 9781441988010

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Analysis on Fock Spaces by Kehe Zhu Pdf

Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces” are by now standard and well established. But the term “Fock spaces” is a different story. Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the author’s, have also appeared in the past few decades. But there has been no book on the market concerning the Fock spaces. The purpose of this book is to fill that void, especially when many results in the subject are complete by now. This book presents important results and techniques summarized in one place, so that new comers, especially graduate students, have a convenient reference to the subject. This book contains proofs that are new and simpler than the existing ones in the literature. In particular, the book avoids the use of the Heisenberg group, the Fourier transform, and the heat equation. This helps to keep the prerequisites to a minimum. A standard graduate course in each of real analysis, complex analysis, and functional analysis should be sufficient preparation for the reader.

Author : Joel H. Shapiro
Publisher : Springer
Page : 223 pages
File Size : 41,9 Mb
Release : 1993-08-26
Category : Mathematics
ISBN : 0387940677

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Composition Operators by Joel H. Shapiro Pdf

The study of composition operators links some of the most basic questions you can ask about linear operators with beautiful classical results from analytic-function theory. The process invests old theorems with new mean ings, and bestows upon functional analysis an intriguing class of concrete linear operators. Best of all, the subject can be appreciated by anyone with an interest in function theory or functional analysis, and a background roughly equivalent to the following twelve chapters of Rudin's textbook Real and Complex Analysis [Rdn '87]: Chapters 1-7 (measure and integra tion, LP spaces, basic Hilbert and Banach space theory), and 10-14 (basic function theory through the Riemann Mapping Theorem). In this book I introduce the reader to both the theory of composition operators, and the classical results that form its infrastructure. I develop the subject in a way that emphasizes its geometric content, staying as much as possible within the prerequisites set out in the twelve fundamental chapters of Rudin's book. Although much of the material on operators is quite recent, this book is not intended to be an exhaustive survey. It is, quite simply, an invitation to join in the fun. The story goes something like this.

Author : Le Hai Khoi,Javad Mashreghi
Publisher : Birkhäuser
Page : 0 pages
File Size : 41,9 Mb
Release : 2023-10-21
Category : Mathematics
ISBN : 3031397037

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Theory of N_p Spaces by Le Hai Khoi,Javad Mashreghi Pdf

This monograph provides a comprehensive study of a typical and novel function space, known as the $\mathcal{N}_p$ spaces. These spaces are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball, and the authors also explore composition operators and weighted composition operators on these spaces. The book covers a significant portion of the recent research on these spaces, making it an invaluable resource for those delving into this rapidly developing area. The authors introduce various weighted spaces, including the classical Hardy space $H^2$, Bergman space $B^2$, and Dirichlet space $\mathcal{D}$. By offering generalized definitions for these spaces, readers are equipped to explore further classes of Banach spaces such as Bloch spaces $\mathcal{B}^p$ and Bergman-type spaces $A^p$. Additionally, the authors extend their analysis beyond the open unit disk $\mathbb{D}$ and open unit ball $\mathbb{B}$ by presenting families of entire functions in the complex plane $\mathbb{C}$ and in higher dimensions. The Theory of $\mathcal{N}_p$ Spaces is an ideal resource for researchers and PhD students studying spaces of analytic functions and operators within these spaces.

Author : Calvin C. Moore,Claude L. Schochet
Publisher : Cambridge University Press
Page : 316 pages
File Size : 52,8 Mb
Release : 2006
Category : Mathematics
ISBN : 0521613051

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Global Analysis on Foliated Spaces by Calvin C. Moore,Claude L. Schochet Pdf

This book presents a complete proof of Connes' Index Theorem generalized to foliated spaces, including coverage of new developments and applications.