T~*=T^2时算子T的谱

Spectrum of Operator T when T~*=T ~2

对自共轭算子的概念加以推广,引进了平方共轭算子的概念.应用希尔伯特空间上正规算子的概念、性质、谱映射定理和类推的方法,研究了该类算子的性质及正则值存在的充要条件.结果表明,当T =T2时,该类算子T的谱是有限的特征谱.

The concept of a selfconjugate operator in Hilbert space was extended by introducing the definition of a conjugate squareoperator. The properties of the operator and the necessary and sufficient conditions for the regular value to exist were studied using the concept and properties of normal operators in Hilbert space, the spectrum mapping principle and analogy. The results obtained show that, when T*=T  2, the spectrum of conjugate squareoperator T is a finite spectrum.