Min-phase-isometries on the unit sphere of Lp-type spaces

Abstract

Let X,Y be two real L_p-spaces (p>0), then a surjective map f:S_X->S_Y satisfies
min{||f(x)+f(y)||,||f(x)-f(y)||} = min{||x+y||,||x−y||} (x,y∈S_X),
if and only if f is a multiplication of a linear isometry and a map with rang {−1,1}. It can be regarded as a new Wigner’s theorem for real L_p-spaces (p>0).