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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

Douglas Bridges  and
Robin Havea
Douglas Bridges
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 1, New Zealand, d.bridges@math.canterbury.ac.nz
Robin Havea
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 1, New Zealand, rha40@student.canterbury.ac.nz

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.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 3 , 2000 , pp. 191 - 206
Copyright
Copyright © London Mathematical Society 2000

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