Linear operators preserving the decomposable numerical range
Marvin D. Marcus, Ivan Filippenko · Linear and Multilinear Algebra · 1979
Multilinear techniques are used to characterize unitary matrices in terms of a generalized numerical range. This characterization is then applied to analyze the structure of all linear operators on matrices which preserve this numerical range. The results generalize V. J. Pellegrini's determination of all linear operators preserving the classical numerical range.