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arXiv · 1701.05538

Approximation in the closed unit ball

Javad Mashreghi·Thomas Ransford
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Abstract

In this expository article, we present a number of classic theorems that serve to identify the closure in the sup-norm of various sets of Blaschke products, inner functions and their quotients, as well as the closure of the convex hulls of these sets. The results presented include theorems of Carath\'eodory, Fisher, Helson-Sarason, Frostman, Adamjan-Arov-Krein, Douglas-Rudin and Marshall. As an application of some of these ideas, we obtain a simple proof of the Berger-Stampfli spectral mapping theorem for the numerical range of an operator.

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Javad Mashreghi, Thomas Ransford. 2017-01-19. Approximation in the closed unit ball. https://arxiv.org/abs/1701.05538

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