某类无穷维Hamilton算子的Moore-Penrose可逆性  

MOORE-PENROSE INVERTIBILITY FOR SOME CLASS OF INFINITE DIMENSIONAL HAMILTONIAN OPERATORS

作　　者：海国君[1] 阿拉坦仓[1] HAI Guo-jun Alatancang(School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《数学杂志》2017年第2期358-364,共7页Journal of Mathematics

基　　金：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)

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 C B-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.Let X be an infinite dimensional Hilbert space, we deno te by H the bounded A C infinite dimensional Hamiltonian operator acting on X ⊕ X of the form H =（A C B-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.

关 键 词：无穷维HAMILTON算子 算子矩阵 Moore-Penrose可逆 

分 类 号：O177.1[理学—数学]