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On the Operator Ranges of Analytic Functions

1983
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Proceedings of the American Mathematical Society
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Following Doob, we say that a function/(z) analytic in the unit disk U has the property K(p) if/(0) = 0 and for some arc y on the unit circle whose measure | y \ > 2p > 0, liminf \f(z])\> 1 where z -: G y and z, E U. J-X Let H be a Hubert space over the complex field, A an operator whose spectrum is included in U, IIAW the operator norm of A. and f(A) the usual Riesz-Dunford operator. We prove that there is no function with the property K( p) satisfying (1 -\\A\\)\\f'(A)\\ « \/n for all IM || <

doi:10.2307/2044359
fatcat:2jkwydrgbbg7ve2uptz6y4vwfi