## Banach Algebra Techniques in the Theory of Toeplitz Operators, Volume 15 |

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Amer Banach algebra bidisk C*-algebra C*-subalgebra class of Toeplitz closure CMn(T Coburn commutative compact operator completes the proof constant contained continuous function COROLLARY cross-section curve denote dim ker essential spectrum exact sequence exists an isometrical extension finite Fourier Fredholm operator function in PC Gohberg Hardy space hence Hilbert space homomorphism homotopic homotopy classes implies inner functions invariant subspaces invertible in AP isometrical isomorphism kernel LC(H LC(M Lemma line segment Malysev mapping Math matrix maximal ideal space mean motion minus the winding modulo the compacts Moreover Neumann algebra obtain operators defined orthogonal projection piecewise continuous problem PROPOSITION prove quarter-plane quotient algebra R. G. Douglas refer the reader result due result follows scalar selfadjoint simply invariant subspace spectral inclusion theorem subset T(AP tion Toeplitz operators topology unilateral shift unitarily equivalent unitary operator vanish von Neumann algebra Wiener-Hopf operators winding number zero