A constructive analysis of a proof that the numerical range is convex
Douglas Bridges and Robin Havea
Abstract: 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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