A Holomorphic Characterization of C*-Algebras

Abstract

Publisher Summary The theory of operator algebras, that is, C*-algebras and von Neumann algebras on complex Hilbert spaces is of increasing importance to many branches of mathematics, for example, integration theory, operator theory, algebraic topology, and particularly mathematical physics and quantum mechanics. Because C*-algebras provide a natural framework for the foundations of quantum mechanics and quantum field theory, it is an important problem to characterize the class of C*-algebras by certain properties, for instance, motivated by physical experiments. Two characterizations of operator algebras in different categories exist: (1) A. Connes' characterization of von Neumann algebras in terms of self-dual homogeneous Hilbert cones and (2) the work of Alfsen and Shultz characterizing the state spaces of C*-algebras using the geometry of compact convex sets and their affine function spaces.