Dichotomy theorems for random matrices and closed ideals of operators on (?n=18l1n)c0
Dichotomy theorems for random matrices and closed ideals of operators on (?n=18l1n)c0
复制标题
(?n=18l1n)c0 上随机矩阵和算子闭合理想的二分定理
DOI：
10.1112/jlms/jdr083
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Laustsen N
中科院分区：
文献类型：
--
作者：
Laustsen N
本文证明了两个关于由随机矩阵给出的L ~ 1的算子序列的二分性定理。在第二个定理中，我们假设每个随机矩阵的元素构成一个独立的对称随机变量序列。则相应的算子序列要么一致因子化恒等算子在k ∈ k（k∈ k）上，要么一致近似因子化通过co.第一定理的结论稍弱，但仍与因子化性质有关，但没有对随机矩阵作任何假设.实际上，它适用于定义在任意序列的Banach空间上的算子。这些结果提供了空间（n=1∞ <$1n）co上所有算子的Banach代数的闭理想结构的信息.
We prove two dichotomy theorems about sequences of operators intoL1given by random matrices. In the second theorem, we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the corresponding sequence of operators either uniformly factor the identity operators on ℓ1k(k∈ℕ) or uniformly approximately factor through co. The first theorem has a slightly weaker conclusion still related to factorization properties, but makes no assumption on the random matrices. Indeed, it applies to operators defined on an arbitrary sequence of Banach spaces. These results provide information on the closed ideal structure of the Banach algebra of all operators on the space (⊕n=1∞ℓ1n)co.