一类闭算子的特征

Characteristic of a kind of Closed Operators

本文引入了闭拟谱算子概念,得到这类闭算子的谱分解特征。推广了Banach空间中纯量型(无界)谱算子以及Well-bounded算子谱分解理论。 主要结果:T为闭拟谱算子的充要条件是T稠定闭,且存在复数u使I_mu≠0以及连续代数同态:Ac_o(R′)—→B(x),使得。

This paper extends the spectral theory of well-bounded operator's and Scalar-type spectral operators to the classes of closed operators, obtains spectral resolution characteristics of such operators. Theorem. T is a closed-quasi-spectral operator, if and only if, T is a density difined closed operator, and there exists a complex number Imu≠0 and a Continous algebra homophism . Ac0(R')→B(X), such that [(u-λ)-1] = R(u; T)