Linear operators preserving the generalized decomposable numerical range

摘要

Linear operator T:C_(n X n)-->C_(n X n) is said to preserve f-decomposable numerical range if W_f(T(A))= W_f(A) for all A∈ C_(n X n). Pellegrini determined the linear operators preserving the classical numerical range. Marcus and Filippenko, Tarn determined the linear operators preserving f-decomposable numerical range for some characters f of degree 1 satisfying certain conditions, However, for a general irreducible character, this linear preserver problem remained solved. In this note we determinethe linear operators preserving f-decomposable numerical range so that the problem is completely solved.