一类反三角算子矩阵的本质谱

The Essential Spectrum of a Class of Anti-Triangular Opera tor Mat rices

该文讨论了一类无界非自伴反三角算子矩阵的本质谱.利用二次算子族及其矩阵内部元素的性质等价刻画了算子矩阵的本质谱,并在此基础上估计了算子矩阵的本质谱的范围.最后基于本质谱的研究,讨论了其非实谱的聚点问题.

In this paper,the essential spectrum of a class of unbounded unself-adjoint anti-triangular operator matrices is studied.Firstly,we describe the essential spectrum of operator matrices by using the quadratic operator pencil and the properties of its operator entries,and estimate the essential spectrum of the whole operator matrix.On this basis,the accumulation point of the non-real spectrum of the operator matrix is analyzed.