| 摘要: |
| 设X是无穷维Hilbert空间， H表示X ⊕ X上的有界无穷维Hamilton算子H=（A CB-A*），其中B和C为自伴算子.本文研究了无穷维Hamilton算子H的Moore-Penrose广义逆.利用空间分解等方法，当B=0或C为Moore-Penrose可逆的情况下给出H为Moore-Penrose可逆的等价条件.此外，举例说明了结论的有效性. |
| 关键词: 无穷维Hamilton算子 算子矩阵 Moore-Penrose可逆 |
| DOI： |
| 分类号:O177.1 |
| 基金项目:国家自然科学基金资助（11371185；11362011）；内蒙古自然科学基金重大项目资助（2013ZD01）；内蒙古自然科学基金（2015MS0117）. |
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| MOORE-PENROSE INVERTIBILITY FOR SOME CLASS OF INFINITE DIMENSIONAL HAMILTONIAN OPERATORS |
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HAI Guo-jun, Alatancang
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School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
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| Abstract: |
| Let X be an infinite dimensional Hilbert space,we denote by H the bounded infinite dimensional Hamiltonian operator acting on X ⊕X of the form H=(A CB -A*),where B and C are self-adjoint operators.In this paper,we consider the Moore-Penrose invertibility of the infinite dimensional Hamiltonian operator.In the case when B=0 or C is Moore-Penrose invertible,by using space decomposition method,the equivalent conditions for H is Moore-Penrose invertible are given.Furthermore,some examples that illustrate the effectiveness of our results are given. |
| Key words: infinite dimensional Hamilton operator operator matrices Moore-Penrose invertibility |
