Linear operators preserving the decomposable numerical radius
Chi-Kwong Li, Nam‐Kiu Tsing · Linear and Multilinear Algebra · 1988
The characterization of all linear operators on matrices which preserve the decomposable numerical radius is obtained. This result refines those of Tam. Marcus and Filippenko on the topic. The proof of the main theorem depends on a characterization of scalar multiples of unitary matrices in terms of decomposable numerical radius that is of independent interest.