中文摘要：

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.

英文摘要：

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.