套代数的直和算子集及可逆算子

Operator Set of Nest Algebra in Direct Sums and Its Invertible Operators

中文关键词:  套代数  期望  可逆算子

英文关键词:nest algebra  expectation  invertible operator

中文摘要:

      本文研究了套代数的一个直和算子集X_N^φ,得到套代数的直和分解:τ(N)=D_N⊕X_N^φ,同时讨论了套代数中可逆算子的分布,得出套代数的对角D_N关于可逆算子是封闭的。特别地,当套为可数套时,套代数关于可逆性算子封闭的充要条件为φ(T)可逆。

英文摘要:

      In this paper, we characterize the properties of X_N^φ, where X_N^φ is an operator set of nest algebra, and show that the direct sum of nest algebra is τ(N) = D_N⊕X_N^φ. We prove also that the invertible element of operators in D_N belongs to D_N. When the nest is a countable nest, we obtain that the invertible element of the operator T in τ(N) belongs to τ(N) if and only if φ(T) is invertible.