Generalized isometries of the special unitary group (Q5964799)

Let \(N(L) \) be a unitary invariant norm on \(M_n\). Assume \(f: {\mathbb T} \to {\mathbb C}\) is a continuous function satisfying certain natural additional properties. Let \(\varphi : SU_n\to SU_n\) be a generalized isometry map with respect to the generalized distance measure \(d_{N,f}\) induced by \(N(L).\) The authors obtain the complete characterization for all such maps \(\varphi\).