A non-injective version of Wigner's theorem
Mark Pankov, Lucijan Plevnik · Operators and Matrices · 2023
Let H be a complex Hilbert space and let F s (H) be the real vector space of all selfadjoint finite rank operators on H . We prove the following non-injective version of Wigner's theorem: every linear operator on F s (H) sending rank one projections to rank one projections (without any additional assumption) is either induced by a linear or conjugate-linear isometry or constant on the set of rank one projections.