An Introduction to C*-Algebras and the Classification Program (Paperback)

Banach algebras and spectral theory.- The Gelfand representation.- C*-algebra basics.- Positive elements.- Positive linear functionals and representations.- Weak and strong operator topologies and von Neumann algebras.- Tensor products for C*-algebras.- Completely positive maps.- Inductive limits and approximately finite (AF) C*-algebras.- Group C*-algebras and crossed products.- Cuntz algebras.- Quasidiagonal C*-algebras.- K-theory for unital C*-algebras.- Classification of AF-algebras.- Nuclear dimension.- Strongly self-absorbing algebras.- The Jiang-Su algebra.- Strict comparison and the Cuntz semigroup.- The Classification Theorem and the Toms-Winter Theorem.