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A Constructive Analysis of a Proof that the Numerical Range is Convex
Published online by Cambridge University Press: 01 February 2010
Abstract
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It is shown where the classical proof of the convexity of the numerical range of an operator on a Hilbert space breaks down by using principles that are not valid in intuitionistic logic. Those breakdowns are then repaired, as far as possible, to provide constructive versions of the convexity theorem. Finally, it is shown that our results are the best possible in a constructive setting.
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- Copyright © London Mathematical Society 2000
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