Some Equivalent Characterizations of the Polynomial Numerical Hull of Degree

Abstract

In this paper we establish several equivalent characterizations, some of which provide a natural distinction between boundary points and interior points, and hence should prove useful for computations. Additionally, we use one of these equivalent definitions to prove that the polynomial numerical hull of any fixed degree for a Toeplitz matrix whose symbol is piecewise continuous approaches all or most of that of the infinite-dimensional Toeplitz operator, as the matrix goes to infinity.