论文标题
规范空间之间的相位图
Phase-isometries between normed spaces
论文作者
论文摘要
令$ x $和$ y $为真实的规范空间，$ f \ colon x \ to y $ a $ $ $ $ $。然后$ f $满足$ \ {\ | f（x）+f（y）\ |，\ | f（x）-f（y）-f（y）\ | \} = \ {\ | x+y \ |，\ | x-y \ \ | \ | \ | \ | \ | \ | \ | \ | \ | \ | \ | \ | \ | \ | $ f =σu$，其中$ u \ u \ colon x \ to y $是滤光的线性等轴测图，$σ\ colon x \ to \ { - 1,1 \} $。这是真正规范空间的Wigner类型结果。
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, $f=σU$, where $U \colon X\to Y$ is a surjective linear isometry and $σ\colon X\to \{-1,1\}$. This is a Wigner's type result for real normed spaces.
