GEOMETRY OF STATE SPACES OF OPERATOR ALGEBRAS

This book provides 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). This material, which has previously only appeared in research papers based on substantial prerequisites, is made accessible to a broad mathematical audience. The necessary prerequisites on C*-algebras and von Neumann algebras are summarized in an appendix, which contains all relevant definitions and results. All necessary background on Jordan algebras is given in the present book, and the first part of the book may be of independent interest for those wanting a quick introduction to Jordan algebras. This work will be of interest to researchers and students in operator algebras.