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The numerical range of functions and best approximation

Published online by Cambridge University Press:  24 October 2008

Lawrence A. Harris
Lawrence A. Harris
Affiliation:
University of Kentucky, Lexington, Kentucky 40506, U.S.A.
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Extract

In this note, we state general conditions which imply that the numerical range of a function mapping a set S into a normed linear space Y is the closed convex hull of the spatial numerical range of the function. This conclusion is of interest since, for example, it is equivalent to an extension to non-compact spaces of Kolmogoroff's characterization of functions of best approximation.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 133 - 141
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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