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

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.
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