论文标题
使用换向器的矩阵分解
Decompositions of matrices by using commutators
论文作者
论文摘要
我们将使用换向器提供$ 3 \ times 3 $矩阵的分解作为总和满足某些偏态身份的总和，并且我们将它们应用于无限等级的免费模块的有限线性运算符和内态性。特别是事实证明，无限尺寸复杂的希尔伯特空间的每个有界的操作员是四个订单$ 3 $的自动形态的总和，而作为无限尺寸矢量空间内态态环的每个简单戒指的总和是其最大理想的无限尺寸矢量空间，这是三个nilpotent subers sup ress sup sup sup sup sup sup。
We will use commutators to provide decompositions of $3\times 3$ matrices as sums whose terms satisfy some polynomial identities, and we apply them to bounded linear operators and endomorphisms of free modules of infinite rank. In particular it is proved that every bounded operator of an infinite dimensional complex Hilbert space is a sum of four automorphisms of order $3$ and that every simple ring that is obtained as a quotient of the endomorphism ring of an infinitely dimensional vector space modulo its maximal ideal is a sum of three nilpotent subrings.
