Geometry of State Spaces of Operator Algebras

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Focusing on the geometric description of state spaces, this book provides axiomatic characterizations of convex sets associated with C*-algebras, von Neumann algebras, and their generalizations, the JB-algebras and JBW-algebras. It emphasizes the significance of these characterizations as a crucial step towards understanding associative algebras. The text includes an updated presentation of key characterization theorems and offers an appendix summarizing essential definitions and results for reader convenience, ensuring the book remains self-contained.