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A problem on the Riesz-Dunford operator calculus and convex univalent functions
Published online by Cambridge University Press: 18 May 2009
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In his paper [3], Ky Fan asked whether if f is a convex univalent function in the unit disk, with f(0) = 0 and f'(0) = 1, then is it true that the set of f(A) is a convex set of operators, when A runs through all proper contractions on a Hilbert space? We answer this question in the negative.
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- Copyright © Glasgow Mathematical Journal Trust 1983
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