| 蔡静,陈果良.Banach空间上有界线性算子的Drazin逆的扰动分析(英文)[J].数学研究及应用,2004,24(3):421~429 |
| Banach空间上有界线性算子的Drazin逆的扰动分析(英文) |
| Perturbation Analysis for the Drazin Inverses of Bounded Linear Operators on a Banach Space |
| 投稿时间：2001-07-03 |
| DOI：10.3770/j.issn:1000-341X.2004.03.008 |
| 中文关键词: Drazin逆 指标 误差界 |
| 英文关键词:Drazin inverse index error bound. |
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| 中文摘要: |
| 设X为一复域C上的Banach空间,设T:X→X为一有界线性算子,其指标为k且R(Tk)闭.记T的Drazin逆为TD.设T=T+δT,则在一定条件下,TD有简明分解式TD=TD(I+δTTD)-1=(I+TDδT)-1TD,从而导出了相对误差‖TD-TD< |
| 英文摘要: |
| Let X be a Banach space over the complex field C and let T : X→X be a bounded linear operator with Ind(T) = k and R(Tk) closed. Denote the Drazin inverse of T by TD. Let T = T + δT, then TD has the simple expression TD = TD(I + δTTD)-1= (I + TDδT)-1TD under certain hypotheses. The upper bound for the relative error ‖TD-TD‖/‖TD‖and for the solution to the operator equation: Tx = u (u∈R(TD)) is also considered. |
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