Abstract
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.
Acknowledgments
The research of Li was partially supported by NSF. Sze would like to thank Dr. Jor-Ting Chan for his guidance and encouragement.
Notes
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