Vector Lattices and Intergal Operators

Semėn Samsonovich Kutateladze

ISBN 10: 9401065713 / ISBN 13: 9789401065719

Editore: Springer Netherlands, 2011

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9789401065719

Dati bibliografici

• Titolo: Vector Lattices and Intergal Operators
• Editore: Springer Netherlands
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 9401065713
• ISBN 13: 9789401065719
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 240 L x 160 A x 26 P (millimetri) 240 millimetri di larghezza per 160 millimetri di altezza per 26 millimetri di profonditą
• Peso: 754 grammi

Descrizione articolo

Riassunto

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.

Contenuti

Foreword. 1. Nonstandard Theory of Vector Lattices; A.G. Kusraev, S.S. Kutateladze. 2. Operator Classes Determined by Order Conditions; A.V. Bukhvalov. 3. Stably Dominated and Stably Regulator Operators; B.M. Makarov. 4. Integral Operators; A.V. Bukhvalov, V.B. Korotkov, B.M. Makarov. 5. Disjointness Preserving Operators; A.E. Gutman. Index.