Symmetric Function Spaces On Atomless Probability Spaces
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Symmetric Function Spaces On Atomless Probability Spaces
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Author : Anatoliĭ M. Plichko
language : en
Publisher:
Release Date : 1990
Symmetric Function Spaces On Atomless Probability Spaces written by Anatoliĭ M. Plichko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Abelian groups categories.
The Rademacher System In Function Spaces
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Author : Sergey V. Astashkin
language : en
Publisher: Springer Nature
Release Date : 2020-07-27
The Rademacher System In Function Spaces written by Sergey V. Astashkin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-27 with Mathematics categories.
This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in Lp-spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces.
Spear Operators Between Banach Spaces
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Author : Vladimir Kadets
language : en
Publisher: Springer
Release Date : 2018-04-16
Spear Operators Between Banach Spaces written by Vladimir Kadets and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-16 with Mathematics categories.
This monograph is devoted to the study of spear operators, that is, bounded linear operators G between Banach spaces X and Y satisfying that for every other bounded linear operator T:X → Y there exists a modulus-one scalar ω such that ǁ G+ωTǁ = 1 + ǁTǁ. This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on L1. The relationships with the Radon-Nikodým property, with Asplund spaces and with the duality, and some isometric and isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz version of the equation above are studied. The book could be of interest to young researchers and specialists in functional analysis, in particular to those interested in Banach spaces and their geometry. It is essentially self-contained and only basic knowledge of functional analysis is needed.
Problems And Recent Methods In Operator Theory
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Author : Fernanda Botelho
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-18
Problems And Recent Methods In Operator Theory written by Fernanda Botelho and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-18 with Functional analysis -- Linear function spaces and their duals -- Banach spaces of continuous, differentiable or analytic functions categories.
This volume contains the proceedings of the Workshop on Problems and Recent Methods in Operator Theory, held at the University of Memphis, Memphis, TN, from October 15–16, 2015 and the AMS Special Session on Advances in Operator Theory and Applications, in Memory of James Jamison, held at the University of Memphis, Memphis, TN, from October 17–18, 2015. Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. It also provides powerful tools for the development of other areas of science including quantum theory, physics and mechanics. Isometries have applications in solid-state physics. Hermitian operators play an integral role in quantum mechanics very much due to their “nice” spectral properties. These powerful connections demonstrate the impact of operator theory in various branches of science. The articles in this volume address recent problems and research advances in operator theory. Highlighted topics include spectral, structural and geometric properties of special types of operators on Banach spaces, with emphasis on isometries, weighted composition operators, multi-circular projections on function spaces, as well as vector valued function spaces and spaces of analytic functions. This volume gives a succinct overview of state-of-the-art techniques from operator theory as well as applications to classical problems and long-standing open questions.
Narrow Operators On Function Spaces And Vector Lattices
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Author : Mikhail Popov
language : en
Publisher: Walter de Gruyter
Release Date : 2012-12-06
Narrow Operators On Function Spaces And Vector Lattices written by Mikhail Popov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Problems In Operator Theory
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Author : Yuri A. Abramovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Problems In Operator Theory written by Yuri A. Abramovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book contains complete solutions to the more than six hundred exercises in the authors' book: Invitation to operator theory--foreword.
An Invitation To Operator Theory
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Author : Yuri A. Abramovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
An Invitation To Operator Theory written by Yuri A. Abramovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
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 very recent developments in operator theory and also draws together results which are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation arepresented 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 importantand useful role in the exposition. They help to free the proofs of the main results of some technical details 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 that includes many well-known results whose proofs are not readily available elsewhere. The companion volume, Problems in Operator Theory, also by Abramovich and Aliprantis, is available from the AMS as Volume 51 inthe Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory. The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts ofsuch details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal. Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, andfunctional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Bothbooks will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.
Ordered Structures And Applications
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Author : Marcel de Jeu
language : en
Publisher: Birkhäuser
Release Date : 2016-09-22
Ordered Structures And Applications written by Marcel de Jeu and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-22 with Mathematics categories.
This book presents the proceedings of Positivity VII, held from 22-26 July 2013, in Leiden, the Netherlands. Positivity is the mathematical field concerned with ordered structures and their applications in the broadest sense of the word. A biyearly series of conferences is devoted to presenting the latest developments in this lively and growing discipline. The lectures at the conference covered a broad spectrum of topics, ranging from order-theoretic approaches to stochastic processes, positive solutions of evolution equations and positive operators on vector lattices, to order structures in the context of algebras of operators on Hilbert spaces. The contributions in the book reflect this variety and appeal to university researchers in functional analysis, operator theory, measure and integration theory and operator algebras. Positivity VII was also the Zaanen Centennial Conference to mark the 100th birth year of Adriaan Cornelis Zaanen, who held the chair of Analysis in Leiden for more than 25 years and was one of the leaders in the field during his lifetime.
Operator And Norm Inequalities And Related Topics
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Author : Richard M. Aron
language : en
Publisher: Springer Nature
Release Date : 2022-08-10
Operator And Norm Inequalities And Related Topics written by Richard M. Aron and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-10 with Mathematics categories.
Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades. Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development. A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.
Haar Series And Linear Operators
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Author : I. Novikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Haar Series And Linear Operators written by I. Novikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
In 1909 Alfred Haar introduced into analysis a remarkable system which bears his name. The Haar system is a complete orthonormal system on [0,1] and the Fourier-Haar series for arbitrary continuous function converges uniformly to this function. This volume is devoted to the investigation of the Haar system from the operator theory point of view. The main subjects treated are: classical results on unconditional convergence of the Haar series in modern presentation; Fourier-Haar coefficients; reproducibility; martingales; monotone bases in rearrangement invariant spaces; rearrangements and multipliers with respect to the Haar system; subspaces generated by subsequences of the Haar system; the criterion of equivalence of the Haar and Franklin systems. Audience: This book will be of interest to graduate students and researchers whose work involves functional analysis and operator theory.