Commutative Banach algebra - Encyclopedia of Mathematics.

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Contents 1. Banach Algebras 1 1.1. Examples 2 1.2. New Banach Algebras from old 6 2. The spectrum 9 2.1. Gelfand-Mazur theorem 11 2.2. The spectral radius formula 12 3. Multiplicative Functionals 15 3.1. Multiplicative Functionals and Ideals 16 3.2. G-K-Z theorem 17 4. The Gelfand Map 19 4.1. Examples 20 4.2. The Spectral Mapping Theorem 20 4.3.