The numerical range of functions and best approximation
Lawrence A. Harris · Mathematical Proceedings of the Cambridge Philosophical Society · 1974
In this note, we state general conditions which imply that the numerical range of a function mapping a setSinto a normed linear spaceYis 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.