Overview

This volume is devoted to modern accomplishments in the field of vector lattices and integral operators which were achieved in Russia since the 1970s. Nonstandard methods are elaborated for the analysis of vector lattices under multiplication by an arbitrary bounded operator for various classes of operators which are defined in terms oforder. Also, several approaches to the solution of the J. von Neumann problem on the conditions for integrability of a linear operator are treated, and full information is given on the solution of some problems posed by P. Halmos and V. Sunder.

Full Product Details

Author:   Semën Samsonovich Kutateladze
Publisher:   Springer
Imprint:   Springer
Edition:   1996 ed.
Volume:   358
Weight:   0.996kg
ISBN:  

9780792338970

ISBN 10:   0792338979
Pages:   462
Publication Date:   31 January 1996
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

Table of Contents

1. Nonstandard Theory of Vector Lattices.- 1. Vector Lattices.- 2. Boolean-Valued Models.- 3. Real Numbers in Boolean–Valued Models.- 4. Boolean-Valued Analysis of Vector Lattices.- 5. Fragments of Positive Operators.- 6. Lattice–Normed Spaces.- Comments.- References.- 2. Operator Classes Determined by Order Conditions.- 1. Ideal Spaces.- 2. The Space of Regular Operators.- 3. Spaces of Vector-Functions.- 4. Dominated Operators.- Comments.- References.- 3. Stably Dominated and Stably Regular Operators.- 1. p–Absolutely Summing Operators.- 2. p–Absolutely Summing Operators in Hilbert Space.- 3. Nuclear Operators.- 4. Stably Dominated Operators.- 5. Coincidence of Some Classes of Operators in the Scale of the Banach Spaces LP.- 6. Nikishin–Maurey Factorization Theorems.- 7. Stably Regular Operators.- 8. Certain Operator Lattices.- 9. Operator Spaces and Local Unconditional Structure.- S. Supplement to Chapter 3.- Comments.- References.- 4. Integral Operators.- 1. Basic Properties of Integral Operators.- 2. Integral Representation of Linear Operators.- 3. Applications of the Criterion for Integral Representability.- 4. Linear Operators and Vector Measures.- 5. Integral Representation of Nonlinear Operators.- 6. Algebraic Properties of Integral Operators.- 7. Universal Integral Operators and Operators with Integral Commutators.- Comments.- References.- S. Supplement to Chapter 4. Integral Operators of Convolution (V.D. Stepanov).- References.- 5. Disjointness Preserving Operators.- 1. Prerequisites.- 2. Order Approximating Sets.- 3. Order Bounded Operators.- 4. The Shadow of an Operator.- 5. Orthomorphisms.- 6. Shift Operators.- 7. Weighted Shift Operator.- 8. Representation of Disjointness Preserving Operators.- 9. Interpretation for the Properties of Operators.-Comments.- References.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions