Algebras 210 19.1 The algebra C(S), 210 19.2 Gelfand compactification, 210 19.3 Absolutely convergent Fourier series, 212 19.4 Analytic functions in the closed unit disk, 213 Analytic functions in the closed polydisk 19.5 Analytic functions in the open unit disk, 214 19.6 Wiener's Tauberian theorem, 215 19.7 Commutative B*-algebras, 221 Historical note, 224 20. Examples of Operators and Their Spectra 20.1 Invertible maps, 226 Boundary points of the spectrum 20.2 Shifts, 229 20.3 Volterra integral operators, 230 20.4 The Fourier transform, 231 21. Compact Maps 21.1 Basic properties of compact maps, 233 Compact maps form a two-sided ideal-Identity plus compact map has index zero 226 233
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