| 关于有界线性算子非负分裂的比较定理 |
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| 引用本文： | 宋永忠.关于有界线性算子非负分裂的比较定理[J].数学学报,1997,40(2):313-318. |
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| 作者姓名： | 宋永忠 |
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| 作者单位： | 南京师范大学数学系 南京210097 |
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| 摘 要： | Marek和Szyld建立了有界线性算子非负分裂的比较定理.他们还提出了严格不等式成立的条件,但没有进行详细证明.本注记首先用几个反例说明那里的保证严格不等式成立的条件是不充分的,然后给出正确的关于严格不等式的比较定理.
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| 关 键 词： | 有界线性算子 非负分裂 比较 |
| 收稿时间： | 1994-1-26 |
| 修稿时间： | 1996-6-27 |
A Note on Comparison Theorems for Splittings of Bounded Operators |
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| Song Yongzhong.A Note on Comparison Theorems for Splittings of Bounded Operators[J].Acta Mathematica Sinica,1997,40(2):313-318. |
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| Authors: | Song Yongzhong |
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| Institution: | Song Yongzhong (Department of Mathematics, Nanjing Normal University, Nanjing 210097, China) |
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| Abstract: | Comparison theorems for nonnegative splittings of bounded linear operators have been presented by Marek and Szyld. Without detailed proofs, they also gave the hypotheses which provide strict inequalities for the comparisons. In this note, several counter examples are given which show that all the hypotheses by Marek and Szyld, which provide strict inequalities, are not sufficient. Then the corrected comparison theorems are proposed. |
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| Keywords: | Bounded linear operator Nonnegative splitting Comparison |
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