Phase-isometries between normed spaces

Aleksej Turnsek, Dijana Ilisevic, Matjaz Omladic

Let $X$ and $Y$ be real normed spaces and $f:X\to Y$ a surjective mapping. Then $f$ satisfies $\{\Vert f(x)+f(y)\Vert ,\Vert f(x)-f(y)\Vert \}=\{\Vert x+y\Vert ,\Vert x-y\Vert \}$, $x,y\in X$, if and o…