Numerical bounds on the Crouzeix ratio for a class of matrices
摘要
We provide numerical bounds on the Crouzeix ratio for KMS matrices A which have a line segment on the boundary of the numerical range. The Crouzeix ratio is the supremum over all polynomials p of the spectral norm of p(A) divided by the maximum absolute value of p on the numerical range of A. Our bounds satisfy the conjecture that this ratio is less than or equal to 2. We also give a precise description of these numerical ranges.