多项式共轭算子T的谱

Spectrum of Polynomial Conjugate Operator T

将Hilbert空间上特殊的正规算子———自共轭算子的概念推广到多项式共轭算子.运用正规算子的性质及其谱特点,通过类推的论证方法,结合Banach代数技巧研究了推广后算子———多项式共轭算子T的谱,得出了该类算子的谱是有限的特征谱.例证表明了这一结果是有效的.

The concept of a special normal operator, self-conjugate operator, in Hilbert space was extended to a polynomial conjugate operator. Based on the properties and spectrum feature of a normal operator in Hilbert space, the spectrum of the extended operator—polynomial conjugate operator T was investigated using the analogy method and the Banach algebra technique. The result shows that the spectrum of the polynomial conjugate operator is a finite eigenvalue spectrum. The conclusion was proved by using an example .