Multiplicative Preservers of C-Numerical Ranges and Radii
نویسنده
چکیده
Multiplicative preservers of C-numerical ranges and radii on certain groups and semigroups of complex n × n matrices are characterized. The general and special linear groups are considered, as well as the semigroups of matrices having ranks not exceeding k, with k fixed in advance. For a fixed C, it turns out that typically the multiplicative preservers of the C-numerical range (or radius) have the form A 7→ f(detA)UAU∗ or, for certain matrices C, the form A 7→ f(detA)UAU∗, for some unitary U and multiplicative map f from the group of nonzero complex numbers to the unit circle.
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