This chapter contains what we consider to be the essentials of non-commutative C*-algebra theory. This is the material that anyone who wants to work seriously with C*-algebras needs to know. The most tractable C*-algebras are those that can be related to compact operators in a certain specific way. These are the so-called GCR algebras, and they are introduced in Section 1.5, after a rather extensive discussion of C*-algebras of compact operators in Section 1.4.
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