极分解定理的注记

海国君, 阿拉坦仓

数学学报 ›› 2018, Vol. 61 ›› Issue (6) : 933-942.

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数学学报 ›› 2018, Vol. 61 ›› Issue (6) : 933-942. DOI: 10.12386/A2018sxxb0084
论文

极分解定理的注记

    海国君, 阿拉坦仓
作者信息 +

A Note on the Polar Decomposition Theorem

    Guo Jun HAI, Alatancang
Author information +
文章历史 +

摘要

HK是Hilbert空间.首先,对给定的算子TBHK),刻画了集合UT={UBHK):U是部分等距算子并且T=UT*T1/2}. 其次,对部分等距算子UBHK),还给出集合TU={TBHK):NT)=NU),RT)=RU),T=UT*T1/2}的刻画. 最后,作为主要结果的应用得到了相关结论.

Abstract

Let H and K be Hilbert spaces. For given TB(H, K), the set UT={UB(H, K):U is a partial isometry and T=U(T*T)1/2} is characterized, and then it is also given that a characterization of TU={TB(H, K):N (T)=N (U), R(T)=R(U), T=U(T*T) 2/1 } for some partial isometry UB(H, K). In addition, as applications of the main results, some related results are obtained.

关键词

算子矩阵 / 极分解 / hypo-EP算子 / Moore-Penreso逆

Key words

operator matrices / polar decomposition / hypo-EP operator / Moore–Penreso inverse

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导出引用
海国君, 阿拉坦仓. 极分解定理的注记. 数学学报, 2018, 61(6): 933-942 https://doi.org/10.12386/A2018sxxb0084
Guo Jun HAI, Alatancang. A Note on the Polar Decomposition Theorem. Acta Mathematica Sinica, Chinese Series, 2018, 61(6): 933-942 https://doi.org/10.12386/A2018sxxb0084

参考文献

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基金

国家自然科学基金资助项目(11761052,11761029);内蒙古自然科学基金资助项目(2015MS0117)

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