Compact Convex Sets and Boundary Integrals

Compact Convex Sets and Boundary Integrals 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 than a decade In fact the in

  • Title: Compact Convex Sets and Boundary Integrals
  • Author: Erik M. Alfsen
  • ISBN: 9783642650116
  • Page: 112
  • Format: Paperback
  • 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 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.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 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 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.

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    • Erik M. Alfsen

      Erik M. Alfsen Is a well-known author, some of his books are a fascination for readers like in the Compact Convex Sets and Boundary Integrals book, this is one of the most wanted Erik M. Alfsen author readers around the world.



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