关于算子谱集理论中的Von Neumann不等式的研究

On the Von Neumann's Inequality in Operator Spectral Theory

首先,应用泛函分析的基本理论给出关于压缩算子的VonNeumann不等式的一个证明.其次,构造了一个Hermitian代数,并说明其中VonNeumann不等式不必成立.再次,应用KyFan的结果把解析函数论中几个简单而重要的结论转化到Hilbert空间算子函数上来.

By using fundamental theory of functional analysis,a new proof of Von Neumann inequality for contraction operator was given. A Hermitian algebra is constructed in which Von Neumann inequality is not true. By virtue of the Ky Fan's results,several simple and important conclusions were constructed from the theory of Holomorphic functions to operator functions in Hilbert space.