Compact Convex Sets and Boundary Integrals

Compact Convex Sets and Boundary Integrals
Author :
Publisher : Springer Science & Business Media
Total Pages : 218
Release :
ISBN-10 : 9783642650093
ISBN-13 : 3642650090
Rating : 4/5 (93 Downloads)

Book Synopsis Compact Convex Sets and Boundary Integrals by : Erik M. Alfsen

Download or read book Compact Convex Sets and Boundary Integrals written by Erik M. Alfsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation theorems of Choquet and Bishop -de Leeuw together with the uniqueness theorem of Choquet inaugurated a new epoch in infinite-dimensional convexity. Initially considered curious and tech nically difficult, these theorems attracted many mathematicians, and the proofs were gradually simplified and fitted into a general theory. The results can no longer be considered very "deep" or difficult, but they certainly remain all the more important. Today Choquet Theory provides a unified approach to integral representations in fields as diverse as potential theory, probability, function algebras, operator theory, group representations and ergodic theory. At the same time the new concepts and results have made it possible, and relevant, to ask new questions within the abstract theory itself. Such questions pertain to the interplay between compact convex sets K and their associated spaces A(K) of continuous affine functions; to the duality between faces of K and appropriate ideals of A(K); to dominated extension problems for continuous affine functions on faces; and to direct convex sum decomposition into faces, as well as to integral for mulas generalizing such decompositions. These problems are of geometric interest in their own right, but they are primarily suggested by applica tions, in particular to operator theory and function algebras.


Compact Convex Sets and Boundary Integrals Related Books

Compact Convex Sets and Boundary Integrals
Language: en
Pages: 218
Authors: Erik M. Alfsen
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly e
Compact Convex Sets and Boundary Integrals
Language: en
Pages: 210
Authors: Erik Magnus Alfsen
Categories: Boundary value problems
Type: BOOK - Published: 195? - Publisher:

DOWNLOAD EBOOK

Introduction to Operator Algebras
Language: en
Pages: 758
Authors: Bing-Ren Li
Categories: Mathematics
Type: BOOK - Published: 1992 - Publisher: World Scientific

DOWNLOAD EBOOK

This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the ba
Integral Representation Theory
Language: en
Pages: 732
Authors: Jaroslav Lukeš
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: Walter de Gruyter

DOWNLOAD EBOOK

This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of functio
State Spaces of Operator Algebras
Language: en
Pages: 362
Authors: Erik M. Alfsen
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations