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9 BH a-1 isz absolutely and uniformly Alg T(A algebra analytic function Banach Banach space BHg(N bounded and analytic bounded linear operator closure compact operators complex number converges absolutely defined denote diagonal cosets diagonal operator diagonal weak divisor of B(z exists finite convolution operators following lemma form T(A Frankfurt and Rovnyak function F H 0 BH half plane Hardy space Hilbert space induces a bounded inner divisor intertwining operators invariant subspaces invertible isometric isomorphism Jtr(CF)Bdx Lat T(A Let A(z Let dim norm Note operators T(A operators with matrix Paley-Wiener theorem polynomials proof is complete quasinilpotent real number s e dsdx scalar valued inner sector similarity theory singular inner function slowly varying functions split subspace of T(A sufficiently large Suppose symbol t)dt univalent valued inner function weak operator topology Weierstrass M-test