Spectraloid operator polynomials, the approximate numerical range and an Eneström–Kakeya theorem in Hilbert space
Volume 198 / 2010
Studia Mathematica 198 (2010), 279-300
MSC: 47A10, 47A56, 47A12.
DOI: 10.4064/sm198-3-7
Abstract
We study a class of operator polynomials in Hilbert space which are spectraloid in the sense that spectral radius and numerical radius coincide. The focus is on the spectrum in the boundary of the numerical range. As an application, the Eneström–Kakeya–Hurwitz theorem on zeros of real polynomials is generalized to Hilbert space.
