Wigner's theorem revisited

Gyula Maksa, Zsolt Páles

In this paper, we give the general solution of the functional equation $$\{\Vert f(x)+f(y)\Vert ,\Vert f(x)-f(y)\Vert \}=\{\Vert x+y\Vert ,\Vert x-y\Vert \}(x,y\in X)$$ where $f:X\to Y$ and…