**by**

**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.**

**Click ****here****
to access the notes.**