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Resumen de Perturbations of the Hºº-calculus

Nigel J. Kalton Árbol académico

  • Suppose A is a sectorial operator on a Banach space X, which admits an H1calculus.

    We study conditions on a multiplicative perturbation B of A which ensure that B also has an H1calculus.

    We identify a class of bounded operators T : X ! X, which we call strongly triangular, such that if B = (1+T)Ais sectorial then it also has anH1calculus.

    In the caseX is a Hilbert space an operator is strongly triangular if and only ifPsn(T)/n < 1where (sn(T))1n=1 are the singular values of T.

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