On Wigner's theorem in strictly convex normed spaces

摘要

In this note we generalize the well-known Wigner's theorem. Let X and Y be real normed spaces and Y strictly convex. We show that f: X → Y satisfies {‖f(s) + f(y)‖,‖f(s)-f(y)‖} = {‖x + y‖, ‖x - y‖}, x,y ∈ X, if and only if f is phase equivalent to a linear isometry.