具有Lipschitz性质的Minkowski空间中的可对角化算子
On diagonalizable operators in Minkowski spaces with the Lipschitz property
摘要：
一个实半内积空间是一个实向量空间$\M$，它配备了一个函数$[.,.] : \M \times \M \to \Re$，该函数在它的第一个变量上是线性的，严格正的，并且满足施瓦茨不等式。众所周知，函数$||x|| = \sqrt{[x,x]}$定义了关于$\M$的范数。反之亦然，对于$X$上的每个范数，都有一个半内积满足这个等式。$\M$上的线性算子$A$称为\emph{adjoint abelian with respect to $[.,.]$}，如果它对每个$x,y \in \M$都满足$[Ax,y]=[x,Ay]$。在满足一定光滑性条件的有限维实半内积空间中，刻画了可对角化的伴随阿贝尔算子。
英文摘要：
A real semi-inner-product space is a real vector space $\M$ equipped with a function $[.,.] : \M \times \M \to \Re$ which is linear in its first variable, strictly positive and satisfies the Schwartz inequality. It is well-known that the function $||x|| = \sqrt{[x,x]}$ defines a norm on $\M$. and vica versa, for every norm on $X$ there is a semi-inner-product satisfying this equality. A linear operator $A$ on $\M$ is called \emph{adjoint abelian with respect to $[.,.]$}, if it satisfies $[Ax,y]=[x,Ay]$ for every $x,y \in \M$. The aim of this paper is to characterize the diagonalizable adjoint abelian operators in finite dimensional real semi-inner-product spaces satisfying a certain smoothness condition.
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