Inclusion Regions for Numerical Ranges and Linear Preservers
Chi-Kwong Li, Nung-Sing Sze · Linear and Multilinear Algebra · 2004
Let R be a proper subset of the complex plane, and let be the set of n×n complex matrices A such that the numerical range W(A) satisfies W(A). Linear maps ϕ on matrices satisfying are characterized. Denote by the set of n×n complex matrices A such that the numerical radius r(A) satisfies r(A) for a proper subset R of nonnegative real numbers. Linear maps ϕ on matrices satisfying are also characterized. Analogous results on Hermitian matrices are obtained.