Phase-isometries on the unit sphere of $C(K)$

Dongni Tan, Yueli Gao

We say that a map $T:S_X\to S_Y$ between the unit spheres of two real normed-spaces $X$ and $Y$ is a phase-isometry if it satisfies \begin{eqnarray*} \{\|T(x)+T(y)\|, \|T(…