Compact Convex Sets And Boundary Integrals

Author : Erik M. Alfsen
Publisher : Springer Science & Business Media
ISBN 13 : 3642650090
Total Pages : 218 pages
Book Rating : 4.93/5 ( download)

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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.

Author : Erik Magnus Alfsen
Publisher :
ISBN 13 : 9780387050904
Total Pages : 210 pages
Book Rating : 4.06/5 ( download)

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Download or read book Compact Convex Sets and Boundary Integrals written by Erik Magnus Alfsen and published by . This book was released on 195? with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Erik Magnus Alfsen (mathématicien).)
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.69/5 ( download)

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Download or read book Compact Convex Sets and Boundary Integrals written by Erik Magnus Alfsen (mathématicien).) and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bing-Ren Li
Publisher : World Scientific
ISBN 13 : 9789810209414
Total Pages : 758 pages
Book Rating : 4.1X/5 ( download)

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Download or read book Introduction to Operator Algebras written by Bing-Ren Li and published by World Scientific. This book was released on 1992 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.

Author : Jaroslav Lukeš
Publisher : Walter de Gruyter
ISBN 13 : 3110203200
Total Pages : 732 pages
Book Rating : 4.02/5 ( download)

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Download or read book Integral Representation Theory written by Jaroslav Lukeš and published by Walter de Gruyter. This book was released on 2010 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications

Author : Erik Magnus Alfsen
Publisher : American Mathematical Soc.
ISBN 13 : 0821818724
Total Pages : 136 pages
Book Rating : 4.25/5 ( download)

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Download or read book Non-Commutative Spectral Theory for Affine Function Spaces on Convex Sets written by Erik Magnus Alfsen and published by American Mathematical Soc.. This book was released on 1976 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we develop geometric notions related to self-adjoint projections and one-sided ideals in operator algebras. In the context of affine function spaces on convex sets we define projective units. P-projections, and projective faces which generalize respectively self-adjoint projections p, the maps a [right arrow] pap, and closed faces of state spaces of operator algebras. In terms of these concepts we state a "spectral axiom" requiring the existence of "sufficiently many" projective objects. We then prove the spectral theorem: that elements of the affine function space admit a unique spectral decomposition. This in turn yields a satisfactory functional calculus, which is unique under a natural minimality requirement (that it be "extreme point preserving").

Author : R. D. Bourgin
Publisher : Springer
ISBN 13 : 3540398732
Total Pages : 485 pages
Book Rating : 4.38/5 ( download)

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Download or read book Geometric Aspects of Convex Sets with the Radon-Nikodym Property written by R. D. Bourgin and published by Springer. This book was released on 2006-11-15 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher : Elsevier
ISBN 13 : 0080532802
Total Pages : 1017 pages
Book Rating : 4.06/5 ( download)

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Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2001-08-15 with total page 1017 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Author : O.B. Bekken
Publisher : Springer
ISBN 13 : 3540382011
Total Pages : 216 pages
Book Rating : 4.10/5 ( download)

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Download or read book Spaces of Analytic Functions written by O.B. Bekken and published by Springer. This book was released on 2006-11-14 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : B. Fuchssteiner
Publisher : Elsevier
ISBN 13 : 9780080871677
Total Pages : 428 pages
Book Rating : 4.74/5 ( download)

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Download or read book Convex Cones written by B. Fuchssteiner and published by Elsevier. This book was released on 2011-08-18 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex Cones