由增重次随机算子及其线性映射确定的$\ell^p(I)^+$的次优化
Submajorization on $\ell^p(I)^+$ determined by increasable doubly substochastic operators and its linear preservers
摘要：
我们注意到Von Neumann \cite{von}的著名结果对离散Lebesgue空间$\ell^p(I)$，$p\in[1,\infty)$上的所有双次随机算子都不成立.这一事实使我们区分两类这些运营商。确切地说，一类增量双次随机算子在$\ell^p(I)$上是孤立的性质，类似的冯诺依曼结果在这类操作是真实的。利用增量次随机算子引入了正锥$\ell^p(I)^+$上的次优控制关系$\prec_s$，当$p\in[1,\infty)$时，次优控制可以看作是偏序.当$I$是无限集时，给出了次优$\prec_s$在$\ell^1(I)^+$和$\ell^p(I)^+$上的两种不同形状的线性映射.
英文摘要：
We note that the well-known result of Von Neumann \cite{von} is not valid for all doubly substochastic operators on discrete Lebesgue spaces $\ell^p(I)$, $p\in[1,\infty)$. This fact lead us to distinguish two classes of these operators. Precisely, the class of increasable doubly substochastic operators on $\ell^p(I)$ is isolated with the property that an analogue of the Von Neumann result on operators in this class is true. The submajorization relation $\prec_s$ on the positive cone $\ell^p(I)^+$, when $p\in[1,\infty)$, is introduced by increasable substochastic operator and it is provided that submajorization may be considered as a partial order. Two different shapes of linear preservers of submajorization $\prec_s$ on $\ell^1(I)^+$ and on $\ell^p(I)^+$, when $I$ is an infinite set, are presented.
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