Ilišević, Dijana ; Omladič, Matjaž ; Turnšek, Aleksej
Let ▫$X$▫ and ▫$Y$▫ be real normed spaces and ▫$f \colon X\to Y$▫ a surjective mapping. Then ▫$f$▫ satisfies ▫$\{\|f(x)+f(y)\|, \|f(x)-f(y)\|\} = \{\|x+y\|, \|x-y\|\}$▫, ▫$x,y\in X$▫, if and only if ...▫$f$▫ is phase equivalent to a surjective linear isometry, that is, ▫$f=\sigma U$▫, where ▫$U \colon X\to Y$▫ is a surjective linear isometry and ▫$\sigma \colon X\to \{-1,1\}$▫. This is a Wigner's type result for real normed spaces.
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