Operator Theory In Function Spaces And Banach Lattices

Author : C.B. Huijsmans,M.A. Kaashoek,W.A.J. Luxemburg,B.de Pagter
Publisher : Birkhäuser
Page : 309 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890762

Get Book

Operator Theory in Function Spaces and Banach Lattices by C.B. Huijsmans,M.A. Kaashoek,W.A.J. Luxemburg,B.de Pagter Pdf

This volume is dedicated to A.C. Zaanen, one of the pioneers of functional analysis, and eminent expert in modern integration theory and the theory of vector lattices, on the occasion of his 80th birthday. The book opens with biographical notes, including Zaanen's curriculum vitae and list of publications. It contains a selection of original research papers which cover a broad spectrum of topics about operators and semigroups of operators on Banach lattices, analysis in function spaces and integration theory. Special attention is paid to the spectral theory of operators on Banach lattices; in particular, to the one of positive operators. Classes of integral operators arising in systems theory, optimization and best approximation problems, and evolution equations are also discussed. The book will appeal to a wide range of readers engaged in pure and applied mathematics.

Author : C.B. Huijsmans,M.A. Kaashoek,W.A.J. Luxemburg,B.de Pagter
Publisher : Birkhäuser
Page : 309 pages
File Size : 50,8 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 3764351462

Get Book

Operator Theory in Function Spaces and Banach Lattices by C.B. Huijsmans,M.A. Kaashoek,W.A.J. Luxemburg,B.de Pagter Pdf

This volume is dedicated to A.C. Zaanen, one of the pioneers of functional analysis, and eminent expert in modern integration theory and the theory of vector lattices, on the occasion of his 80th birthday. The book opens with biographical notes, including Zaanen's curriculum vitae and list of publications. It contains a selection of original research papers which cover a broad spectrum of topics about operators and semigroups of operators on Banach lattices, analysis in function spaces and integration theory. Special attention is paid to the spectral theory of operators on Banach lattices; in particular, to the one of positive operators. Classes of integral operators arising in systems theory, optimization and best approximation problems, and evolution equations are also discussed. The book will appeal to a wide range of readers engaged in pure and applied mathematics.

Author : Kehe Zhu
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 41,6 Mb
Release : 2007
Category : Function spaces
ISBN : 9780821839652

Get Book

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 : Adriaan C. Zaanen
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642606373

Get Book

Introduction to Operator Theory in Riesz Spaces by Adriaan C. Zaanen Pdf

Since the beginning of the thirties a considerable number of books on func tional analysis has been published. Among the first ones were those by M. H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text books. Therefore, authors of textbooks usually restrict themselves to normed spaces (or even to Hilbert space exclusively) and linear operators in these spaces. In more advanced texts Banach algebras and (or) topological vector spaces are sometimes included. It is only rarely, however, that the notion of order (partial order) is explicitly mentioned (even in more advanced exposi tions), although order structures occur in a natural manner in many examples (spaces of real continuous functions or spaces of measurable function~). This situation is somewhat surprising since there exist important and illuminating results for partially ordered vector spaces, in . particular for the case that the space is lattice ordered. Lattice ordered vector spaces are called vector lattices or Riesz spaces. The first results go back to F. Riesz (1929 and 1936), L. Kan torovitch (1935) and H. Freudenthal (1936).

Author : Mikhail Popov,Beata Randrianantoanina
Publisher : Walter de Gruyter
Page : 336 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783110263343

Get Book

Narrow Operators on Function Spaces and Vector Lattices by Mikhail Popov,Beata Randrianantoanina Pdf

Most classes of operators that are not isomorphic embeddings are characterized by some kind of a “smallness” condition. Narrow operators are those operators defined on function spaces that are “small” at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems.

Author : Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis
Publisher : Springer
Page : 616 pages
File Size : 50,9 Mb
Release : 2018-02-14
Category : Mathematics
ISBN : 9783319698083

Get Book

Analysis in Banach Spaces by Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis Pdf

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Author : M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Publisher : Springer Nature
Page : 654 pages
File Size : 46,7 Mb
Release : 2021-03-31
Category : Mathematics
ISBN : 9783030519452

Get Book

Operator Theory, Functional Analysis and Applications by M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich Pdf

This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

Author : S. Okada,Werner J. Ricker,Enrique A. Sánchez Pérez
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 44,8 Mb
Release : 2008-09-09
Category : Mathematics
ISBN : 9783764386481

Get Book

Optimal Domain and Integral Extension of Operators by S. Okada,Werner J. Ricker,Enrique A. Sánchez Pérez Pdf

This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Most of the material appears in print for the first time. The book has an interdisciplinary character and is aimed at graduates, postgraduates, and researchers in modern operator theory.

Author : H.H. Schaefer
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642659706

Get Book

Banach Lattices and Positive Operators by H.H. Schaefer Pdf

Author : Yuri A. Abramovich,Y. Abramovich,Charalambos D. Aliprantis
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 47,7 Mb
Release : 2002
Category : Operator theory
ISBN : 9780821821473

Get Book

Problems in Operator Theory by Yuri A. Abramovich,Y. Abramovich,Charalambos D. Aliprantis Pdf

This book contains complete solutions to the more than six hundred exercises in the authors' book: Invitation to operator theory--foreword.

Author : Yuri A. Abramovich,Charalambos D. Aliprantis
Publisher : Unknown
Page : 530 pages
File Size : 46,8 Mb
Release : 1900
Category : Operator theory
ISBN : 1470420996

Get Book

An Invitation to Operator Theory by Yuri A. Abramovich,Charalambos D. Aliprantis Pdf

This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices using their topological and order structures and properties. Abramovich and Aliprantis give a unique presentation that includes many new and recent advances in operator theory and brings together results that are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time. The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the presentation. They help to free the proofs of the main results of technical details, which are secondary to the principal ideas, but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material, and among them there are many well-known results whose proofs are not readily available elsewhere. Prerequisites are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. The volume is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. It will also be of great interest to researchers in mathematics, as well as in physics, economics, finance, engineering, and other related areas. The companion volume, Problems in Operator Theory, containing complete solutions to all exercises in An Invitation to Operator Theory, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series.

Author : Pei-Kee Lin
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 46,9 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9780817681883

Get Book

Köthe-Bochner Function Spaces by Pei-Kee Lin Pdf

This monograph is devoted to the study of Köthe–Bochner function spaces, an active area of research at the intersection of Banach space theory, harmonic analysis, probability, and operator theory. A number of significant results---many scattered throughout the literature---are distilled and presented here, giving readers a comprehensive view of the subject from its origins in functional analysis to its connections to other disciplines. Considerable background material is provided, and the theory of Köthe–Bochner spaces is rigorously developed, with a particular focus on open problems. Extensive historical information, references, and questions for further study are included; instructive examples and many exercises are incorporated throughout. Both expansive and precise, this book’s unique approach and systematic organization will appeal to advanced graduate students and researchers in functional analysis, probability, operator theory, and related fields.

Author : C.B. Huijsmans,Wilhelm A.J. Luxemburg
Publisher : Springer Science & Business Media
Page : 151 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401727211

Get Book

Positive Operators and Semigroups on Banach Lattices by C.B. Huijsmans,Wilhelm A.J. Luxemburg Pdf

During the last twenty-five years, the development of the theory of Banach lattices has stimulated new directions of research in the theory of positive operators and the theory of semigroups of positive operators. In particular, the recent investigations in the structure of the lattice ordered (Banach) algebra of the order bounded operators of a Banach lattice have led to many important results in the spectral theory of positive operators. The contributions contained in this volume were presented as lectures at a conference organized by the Caribbean Mathematics Foundation, and provide an overview of the present state of development of various areas of the theory of positive operators and their spectral properties. This book will be of interest to analysts whose work involves positive matrices and positive operators.

Author : Fernanda Botelho
Publisher : American Mathematical Soc.
Page : 183 pages
File Size : 54,8 Mb
Release : 2019-10-04
Category : Education
ISBN : 9781470448950

Get Book

Recent Trends in Operator Theory and Applications by Fernanda Botelho Pdf

This volume contains the proceedings of the workshop on Recent Trends in Operator Theory and Applications (RTOTA 2018), held from May 3–5, 2018, at the University of Memphis, Memphis, Tennessee. The articles introduce topics from operator theory to graduate students and early career researchers. Each such article provides insightful references, selection of results with articulation to modern research and recent advances in the area. Topics addressed in this volume include: generalized numerical ranges and their application to study perturbation of operators, and connections to quantum error correction; a survey of results on Toeplitz operators, and applications of Toeplitz operators to the study of reproducing kernel functions; results on the 2-local reflexivity problem of a set of operators; topics from the theory of preservers; and recent trends on the study of quotients of tensor product spaces and tensor operators. It also includes research articles that present overviews of state-of-the-art techniques from operator theory as well as applications to recent research trends and open questions. A goal of all articles is to introduce topics within operator theory to the general public.

Author : Edward E., Jr. Odell,Haskell P. Rosenthal
Publisher : Springer
Page : 211 pages
File Size : 53,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540474937

Get Book

Functional Analysis by Edward E., Jr. Odell,Haskell P. Rosenthal Pdf

The papers in this volume yield a variety of powerful tools for penetrating the structure of Banach spaces, including the following topics: the structure of Baire-class one functions with Banach space applications, operator extension problems, the structure of Banach lattices tensor products of operators and Banach spaces, Banach spaces of certain classes of Fourier series, uniformly stable Banach spaces, the hyperplane conjecture for convex bodies, and applications of probability theory to local Banach space structure. With contributions by: R. Haydon, E. Odell, H. Rosenthal: On certain classes of Baire-1 functions with applications to Banach space theory.- K. Ball: Normed spaces with a weak-Gordon-Lewis property.- S.J. Szarek: On the geometry of the Banach-Mazur compactum.- P. Wojtaszczyk: Some remarks about the space of measures with uniformly bounded partial sums and Banach-Mazur distances between some spaces of polynomials.- N. Ghoussoub, W.B. Johnson: Operators which factor through Banach lattices not containing co.- W.B. Johnson, G. Schechtman: Remarks on Talagrand's deviation inequality for Rademacher functions.- M. Zippin: A Global Approach to Certain Operator Extension Problems.- H. Knaust, E. Odell: Weakly null sequences with upper lp-estimates.- H. Rosenthal, S.J. Szarek: On tensor products of operators from Lp to Lq.- T. Schlumprecht: Limited Sets in Injective Tensor Products.- F. Räbiger: Lower and upper 2-estimates for order bounded sequences and Dunford-Pettis operators between certain classes of Banach lattices.- D.H. Leung: Embedding l1 into Tensor Products of Banach Spaces.- P. Hitczenko: A remark on the paper "Martingale inequalities in rearrangement invariant function spaces" by W.B. Johnson, G. Schechtman.- F. Chaatit: Twisted types and uniform stability.