John Erdos

King's College London

These notes form an introductory account of C*-algebras. Sections 1, 2, and 4 provide a straightforward development of the subject up to the Gelfand-Naimark Theorem, namely the result that every C*-algebra is isometrically isomorphic to a *-subalgebra of the algebra of operators on some Hilbert space. Some results on more general commutative Banach algebras, whose proofs require little extra effort, are included. In Section 3 there are accounts of two applications of the commutative theory: the C*-algebra approach to the spectral theorem for bounded normal operators on Hilbert space and a brief introduction to the ideas of abstract harmonic analysis.

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