利用矩阵范数、矩阵的奇异值、非负矩阵的理论及友矩阵为工具,对定义在Hilbert空间上H的算子多项式的谱的范围进行了刻画.
Let H be complex Hilbert spaces. P(λ )=λ^mAm +λ^m-1Am-1 + ... +A0 is operator polynomial of order m, where A∈ E H( H), i = 0, 1 ,..., m, A≠0. The Spectrum of operator polynomial P (A) is studied by u-sing matrix norm, matrix singular value, and the theory of non-negative matrix.