Integral representation of states on a C*-algebras

Ruelle, David



Abstract : Let E be the compact set of states on a C?-algebra U with identity. We discuss the representations of a state ? as barycenter of a probability measure ? on E. Examples of such representations are the central decomposition and the ergodic decomposition. They are associated with an Abelian von Neumann algebra B in the commutant ?(U)? of the image of U in the representation canonically associated with ?. This situation is studied in general and a number of applications are discussed.




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RUELLE, “Integral representation of states on a C*-algebras,” Archives de l'IHES, consulté le 30 mai 2024,