Department of Mathematics Texas A&M University College Station, Texas 77843 USA
Abstract:
The numerical range of an n × n matrix T is the image of T under a certain set of linear functionals—a set that comprises the extreme points among the states (i.e., norm-one, positive linear functionals) on the n × n matrices—and is convex, by the Toeplitz-Hausdorff theorem. One can view this convexity as a consequence of T's numerical range being equal to a manifestly convex set, the image of T under all states. Taking this view leads us to ask whether a similar result holds when we replace the n × n matrices by a finite dimensional Banach space
