Geometry of State Spaces of Operator Algebras

This monograph presents a complete and self-contained solution to the long-standing problem of giving a geometric description of state spaces of C*-algebras and von Neumann algebras, and of their Jordan algebraic analogs (JB-algebras and JBW-algebras). The material, which previously has appeared only in research papers and required substantial prerequisites for a reader's understanding, is made accessible here to a broad mathematical audience. Geometry of State Spaces of Operator Algebras is intended for specialists in operator algebras, as well as graduate students and mathematicians in other areas.

Gives a quick introduction to Jordan algebras; no previous knowledge is assumed and all necessary background on the subject is given A discussion of dynamical correspondences, which tie together Lie and Jordan structures, and relate the observables and the generators of time evolution in physics Chapters conclude with notes placing the material in historical context

Inhalt
I: Jordan Algebras and Their State Spaces.- 1: JB-algebras.- 2: JBW-algebras.- 3: Structure of JBW-algebras.- 4: Representations of JB-algebras.- 5: State Spaces of Jordan Algebras.- 6: Dynamical Correspondences.- II: Convexity and Spectral Theory.- 7: General Compressions.- 8: Spectral Theory.- III: State Space Characterizations.- 9: Characterization of Jordan Algebra State Spaces.- 10: Characterization of Normal State Spaces of von Neumann Algebras.- 11: Characterization of C*-algebra State Spaces.