论文标题:算子的逼近理论
Approximation of Aperators
论文作者
论文导师 詹兴致,论文学位 硕士,论文专业 计算数学
论文单位 华东师范大学,点击次数 112,论文页数 41页File Size610K
2006-05-01论文网 http://www.lw23.com/lunwen_891629782/
complex Hilbert space; operators; operator norm; positive approximants; positive contraction approximants
本文主要研究的是算子的正逼近问题。给定一个算子A，计算δ(A)=inf{‖A-P‖：P≥0}，并且求出达到下确界的P，就是算子的正逼近问题。本文主要解决了Halmos[2]中提出的一个问题：对于A=(?)，可解出P_0=1/2(?)是其一个正逼近，并且通过理论上的分析，P_0应该是A唯
The main purpose of this paper is to study Postive Approximants of Operators. Given an operator A, determine δ(A) = inf{||A- P||: P ≥ 0}and find a P for which the infimum is attained. We mainly resolve a prob-lem in Halmos[2]: for A = , we can compute P_0 =is a positive approximant of A, and from theory analysis, P_0 should be the unique approximant of A. But he hasn"t proved this. We prove that P_0 is the unique positive approximant of A. For some special sorts A, for example, A is a normal operator, or an Hermitian operator ect. we study the unique condition of positive approximants. For other sorts of approximants of A, we study some. For example, for a normal operator A, its positive contracion approximants and its unique condition.
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