Titlebook: An Introduction to C*-Algebras and the Classification Program; Karen R. Strung,Francesc Perera Textbook 2021 The Editor(s) (if applicable)

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https://doi.org/10.1007/978-3-642-94286-0Approximately finite (AF) C*-algebras were introduced in Chapter 8. The aim of this chapter is to show that separable unital AF algebras can be classified by their pointed ordered K.-groups.

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Einrichtung der ArbeitsgerichteWe saw in Chapter 12 that via the K.-group of a C*-algebra we are able to determine important information by studying the structure of its projections. The more projections a C*-algebra has, the more information we can gain from its K-theory.

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Martin Meyer,Harro Aurin,Horst RummelfängerIn this final chapter, we will connect the material in previous chapters using the framework of the classification program for simple separable nuclear C*-algebras.

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Positive elements,Positive elements play a very important role in the theory of C*-algebras. They allow us to define a partial order on the self-adjoint elements which is a key part of the structure of any C*-algebra.

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Von Neumann algebras and irreducible representations,For any Hilbert space H, the bounded operators B(H) admit topologies distinct the norm topology. We will be interested in the weak operator and the strong operator topologies.

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