完备空间中基于弱拓扑的算子的点谱

Point Spectrum of Operators Based on Weak Topology in Complete Space

运用完备空间中非自共轭紧算子特征值的变分法,在Banach空间和H ilbert空间中讨论了基于弱拓扑的算子的点谱,在不要求算子具有紧性的条件下,运用代数拓扑的方法,将完备空间中的算子的点谱进一步推广,推导过程与算子空间的特征子空间的拓扑性质无关.

Variational method of characteristic value of non-self-conjugate compact operators in complete sPace is used, and the point spectrum of operators based on weak topology has been discussed in Banach space and Hilbert space . The point spectrum of operators in complete space is generalized further without the condition of compactness to the operators using the method of algebraic topology ; generalizations are out of all relation to topology characteristic of the proper subspaces of operator spaces.