Download or read book Representation of Operators on Banach Lattices written by Ramadan Mohamed Jehaima and published by . This book was released on 1987 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Banach Lattices and Positive Operators written by H.H. Schaefer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Positive Operators and Semigroups on Banach Lattices written by C.B. Huijsmans and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Representation Theorems of Abstract Banach Lattices written by María Aránzazu Juan Blanco and published by LAP Lambert Academic Publishing. This book was released on 2012-02 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The space of integrable functions with respect to a vector measure finds applications in important problems as the integral representation and the study of the optimal domain of linear operators or the representation of abstract Banach lattices as spaces of functions. Classical vector measures are defined on a -algebra and with values in a Banach space. However, this framework is not enough for applications to operators on spaces which do not contain the characteristic functions of sets or Banach lattices without weak unit. These cases require the vector measure to be defined on a -ring. In this work we are mainly interested in providing the properties which guarantee the representation of a Banach lattice by means of an space of integrable functions with respect to a vector measure on a -ring. The analytic properties of a vector measure are directly related to the lattice properties of the space L1. It will be also the aim of this work to study the effect of certain properties of the vector measure on the lattice structure of the space L1w. We also study the spaces Lp, Lpw for a vector measure on a -ring and the corresponding representation theorems by means of these spaces.
Download or read book Vector Lattices and Intergal Operators written by Semën Samsonovich Kutateladze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of vector lattices, stemming from the mid-thirties, is now at the stage where its main achievements are being summarized. The sweeping changes of the last two decades have changed its image completely. The range of its application was expanded and enriched so as to embrace diverse branches of the theory of functions, geometry of Banach spaces, operator theory, convex analysis, etc. Furthermore, the theory of vector lattices was impregnated with principally new tools and techniques from other sections of mathematics. These circumstances gave rise to a series of mono graphs treating separate aspects of the theory and oriented to specialists. At the same time, the necessity of a book intended for a wider readership, reflecting the modern diretions of research became clear. The present book is meant to be an attempt at implementing this task. Although oriented to readers making their first acquaintance with vector-lattice theory, it is composed so that the main topics dealt with in the book reach the current level of research in the field, which is of interest and import for specialists. The monograph was conceived so as to be divisible into two parts that can be read independently of one another. The first part is mainly Chapter 1, devoted to the so-called Boolean-valued analysis of vector lattices. The term designates the applica tion of the theory of Boolean-valued models by D. Scott, R. Solovay and P.
Download or read book Narrow Operators on Function Spaces and Vector Lattices written by Mikhail Popov and published by Walter de Gruyter. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Relationships of Positive Operators and Various Functional Representations of Banach Lattices written by Paula G. Young and published by . This book was released on 1993 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Theory in Function Spaces and Banach Lattices written by C.B. Huijsmans and published by Birkhäuser. This book was released on 2012-12-06 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lattice Structures on Banach Spaces written by Nigel John Kalton and published by American Mathematical Soc.. This book was released on 1993 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general problem addressed in this work is to characterize the possible Banach lattice structures that a separable Banach space may have. The basic questions of uniqueness of lattice structure for function spaces have been studied before, but here the approach uses random measure representations for operators in a new way to obtain more powerful conclusions.
Download or read book Banach Lattices written by Peter Meyer-Nieberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Banach Lattices and Operators written by Hans-Ulrich Schwarz and published by . This book was released on 1984 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book History of Banach Spaces and Linear Operators written by Albrecht Pietsch and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Download or read book An Invitation to Operator Theory written by Yuri A. Abramovich and published by . This book was released on 1900 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dominated Operators written by A.G. Kusraev and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of a dominated or rnajorized operator rests on a simple idea that goes as far back as the Cauchy method of majorants. Loosely speaking, the idea can be expressed as follows. If an operator (equation) under study is dominated by another operator (equation), called a dominant or majorant, then the properties of the latter have a substantial influence on the properties of the former . Thus, operators or equations that have "nice" dominants must possess "nice" properties. In other words, an operator with a somehow qualified dominant must be qualified itself. Mathematical tools, putting the idea of domination into a natural and complete form, were suggested by L. V. Kantorovich in 1935-36. He introduced the funda mental notion of a vector space normed by elements of a vector lattice and that of a linear operator between such spaces which is dominated by a positive linear or monotone sublinear operator. He also applied these notions to solving functional equations. In the succeedingyears many authors studied various particular cases of lattice normed spaces and different classes of dominated operators. However, research was performed within and in the spirit of the theory of vector and normed lattices. So, it is not an exaggeration to say that dominated operators, as independent objects of investigation, were beyond the reach of specialists for half a century. As a consequence, the most important structural properties and some interesting applications of dominated operators have become available since recently.
Download or read book Operator Theory in Function Spaces and Banach Lattices written by C.B. Huijsmans and published by Birkhäuser. This book was released on 1995-01-27 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Boolean Valued Analysis written by A.G. Kusraev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.
Download or read book Representation Theorems on Banach Function Spaces written by Neil E. Gretsky and published by American Mathematical Soc.. This book was released on 1968 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
