论文标题
在平滑规范空间中的Wigner定理上
On Wigner's theorem in smooth normed spaces
论文作者
论文摘要
在本说明中，我们概括了著名的Wigner的统一性\独立定理。 For $X$ and $Y$ smooth normed spaces and $f:X\to Y$ a surjective mapping such that $|[f(x),f(y)]|=|[x,y]|$, $x,y\in X$, where $[\cdot,\cdot]$ is the unique semi-inner product, we show that $f$ is phase equivalent to either a linear or an anti-linear surjective isometry.当$ x $和$ y $是平稳的真实规范空间和$ y $ riltery convex时，我们表明wigner的定理等于$ \ {\ | f（x）+f（y）\ |，\ | f（x）-f（x）-f（x）-f（y）-f（y）\ | \ | \ | \ | \ | x $。
In this note we generalize the well-known Wigner's unitary-anti\-unitary theorem. For $X$ and $Y$ smooth normed spaces and $f:X\to Y$ a surjective mapping such that $|[f(x),f(y)]|=|[x,y]|$, $x,y\in X$, where $[\cdot,\cdot]$ is the unique semi-inner product, we show that $f$ is phase equivalent to either a linear or an anti-linear surjective isometry. When $X$ and $Y$ are smooth real normed spaces and $Y$ strictly convex, we show that Wigner's theorem is equivalent to $\{\|f(x)+f(y)\|,\|f(x)-f(y)\|\}=\{\|x+y\|,\|x-y\|\}$, $x,y\in X$.
