摘要
本文证明了以下结论:算子关于一秩投影的绝对方差的绝对值的上确界等于这个算子到所有数乘算子的距离的平方;一个密度算子是忠实的当且仅当它是单射;算子列在密度算子ρ的值域的闭包上的强收敛性蕴含它关于ρ的a.s.收敛性;如果算子列关于每个密度算子是a.s.收敛的,那么它一定是强收敛的;算子列{An}强收敛于A当且仅当它是一致有界的且关于某个忠实的密度算子ρa.s.收敛于A。
The following conclusions are established in this paper. The supremum of the absolute value of the absolute variances of an operator in a rank-one projection is equal to the square of the distance from the operator to the scalar operators; a density operator is faithful if and only if it is injective; the strong convergence on the closure of the range of a density operator ρ implies the ρ-a.s, convergence of the sequence; a sequence of operators is strongly convergent if it is ρ-a.s, convergent for every density operator ρ; if ρ is a faithful density operator, then a sequence operators is strongly convergent to A if and only if it is uniformly bounded and convergent to A a.s. [ρ].
出处
《工程数学学报》
CSCD
北大核心
2010年第1期168-172,共5页
Chinese Journal of Engineering Mathematics
基金
The NNSF of China (10871224
10571113
10826081)
关键词
期望
方差
密度算子
强收敛性
a.s.收敛性
expectation
variance
density operator
strong convergence
a.s. convergence
