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Narrow Operators on Function Spaces and Vector Lattices

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 343/5 ( reviews)

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Book Synopsis Narrow Operators on Function Spaces and Vector Lattices by : Mikhail Popov

Download or read book Narrow Operators on Function Spaces and Vector Lattices written by Mikhail Popov. This book was released on 2012-12-06. 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.

Vector Lattices and Intergal Operators

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 95X/5 ( reviews)

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Book Synopsis Vector Lattices and Intergal Operators by : Semën Samsonovich Kutateladze

Download or read book Vector Lattices and Intergal Operators written by Semën Samsonovich Kutateladze. This book was released on 2012-12-06. 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.

Nonstandard Analysis and Vector Lattices

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 195/5 ( reviews)

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Book Synopsis Nonstandard Analysis and Vector Lattices by : Semen Samsonovich Kutateladze

Download or read book Nonstandard Analysis and Vector Lattices written by Semen Samsonovich Kutateladze. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects applications of nonstandard methods to the theory of vector lattices. Primary attention is paid to combining infinitesimal and Boolean-valued constructions of use in the classical problems of representing abstract analytical objects, such as Banach-Kantorovich spaces, vector measures, and dominated and integral operators. The book is a complement to Volume 358 of MIA Vector Lattices and Integral Operators, printed in 1996.

Operator Theory in Function Spaces and Banach Lattices

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 761/5 ( reviews)

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Book Synopsis Operator Theory in Function Spaces and Banach Lattices by : C.B. Huijsmans

Download or read book Operator Theory in Function Spaces and Banach Lattices written by C.B. Huijsmans. This book was released on 2012-12-06. 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.

Banach Lattices and Positive Operators

1974-12-16 Mathematics
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Release : 1974-12-16
Genre : Mathematics
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Book Synopsis Banach Lattices and Positive Operators by : H.H. Schaefer

Download or read book Banach Lattices and Positive Operators written by H.H. Schaefer. This book was released on 1974-12-16. Available in PDF, EPUB and Kindle. Book excerpt: Vector lattices-also called Riesz spaces, K-lineals, or linear lattices-were first considered by F. Riesz, L. Kantorovic, and H. Freudenthal in the middle nineteen thirties; thus their early theory dates back almost as far as the beginning of the systematic investigation of Banach spaces. Schools of research on vector lattices were subsequently founded in the Soviet Union (Kantorovic, Judin, Pinsker, Vulikh) and in Japan (Nakano, Ogasawara, Yosida); other important contri­ butions came from the United States (G. Birkhoff, Kakutani, M. H. Stone). L. Kantorovic and his school first recognized the importance of studying vector lattices in connection with Banach's theory of normed vector spaces; they investigated normed vector lattices as well as order-related linear operators between such vector lattices. (Cf. Kantorovic-Vulikh-Pinsker [1950] and Vulikh [1967].) However, in the years following that early period, functional analysis and vector lattice theory began drifting more and more apart; it is my impression that "linear order theory" could not quite keep pace with the rapid development of general functional analysis and thus developed into a theory largely existing for its own sake, even though it had interesting and beautiful applications here and there.

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