块算子矩阵限制的二次数值值域

On the Quadratic Numerical Range of Block Operator Matrices

设Γ关于Hilbert空间H1 H2 具有块算子矩阵表示 ,M是Γ的闭不变子空间。讨论了Γ对M限制的二次数值值域 ,Γ的有限直和的二次数值值域及Γ的二次数值值域与不变子空间的关系。

Let Γ be a block operator matrices with respect to Hilbert space H 1H 2, M be a closed invariant subspace of Γ. In this paper,we discuss the quadratic numerical range of the restriction Γ to M, the quadratic numerical range of finitely direct sum of Γ, the relation of the quadratic numerical range with invariant subspace.