Abstract
AbstractContinuing on from where the topic was introduced in Chapter 7, this chapter focuses exclusively on the topic of C*-algebras. One highlight of this chapter is the non-commutative Gelfand–Naimark theorem, which states that every C*-algebra has a faithful representation on some Hilbert space. The chapter discusses notation and examples, and further covers the continuous operational calculus. It investigates *-homomorphisms, positivity of elements, approximate identities, ideals, positive linear functionals, representations, and the Gelfand–Naimark–Segal construction, and its representation associated with a state. We also discuss pure states and two decomposition theorems. Finally, the chapter offer exercises to challenge the reader.
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