## Banach algebras: an introduction |

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absolutely convergent Banach space bounded linear operators C*-algebra carrier space Chapter closure commutative Banach algebra commutative C*-algebra compact Hausdorff space complex field complex numbers complex plane complex-valued cone contained continuous functions COROLLARY define DEFINITION denote divisor of zero element h exists finite Gelfand representation Gelfand topology group algebra Hausdorff space Hence hermitian Banach algebra Hilbert space homomorphism idempotent identity Inasmuch inverse involution isomorphism ji(x kernel Let h linear space locally compact mapping maximal commutative subalgebra minimal idempotent minimal left ideal minimal right ideal modular maximal ideal multiplicative linear functional neighborhood never zero non-trivial m.l.f. non-zero normed algebra NOTATION o,oo positive integer positive linear functional PROOF PROPOSITION quasi-inverse quasi-regular radical real number s.a. element scalar self-adjoint element semi-simple sequence socle sp(h sp(v sp(x spA(x spectrum Stone topology sufficient to show Suppose Theorem 6.7 two-sided ideal unital Banach algebra