一类无穷维Hamilton算子的Fredholm性及本质谱

The Property of Fredholm and Essential Spectrum of a Class of Infinite Dimension Hamiltonian Operator

讨论了一类无穷维Hamilton算子的Fredholm性,由于无穷维Hamilton算子是分块算子矩阵,将它的Fredholm性用它的元素算子的某种组合来描述,给出了无穷维Hamilton算子是Fredholm算子的充分必要条件.

In this article we discuss the property of fredholm of a class of infinite dimension Hamiltonian operator.We describe the property of fredholm of a class of infinite dimension Hamiltonian operator with one combination of its elements of operator.we obtain a necessary and sufficient condition of the property of fredholm of a class of infinite dimension Hamiltonian operator,and give a example.