非自伴算子代数的换位子

Commutators of Non-Self-Adjoint Operator Algebras

中文关键词:  Nest代数  TAF代数  换位子.

英文关键词:Nest algebra  TAF algebra  commutator.

中文摘要:

      设$T$是复数域上的代数, $T$的换位子$[T,T]$指$\{[a,b]:a,b\in T\}$的线性扩张.本文给出了Nest代数$T(N)$的换位子$[T(N),T(N)]$的$\sigma$-弱算子拓扑闭包$\overline{[T(N),T(N)]}^{\sigma -wot}$的刻画,和TAF代数$T$的换位子$[T,T]$的范数闭包$\overline{[T,T]}$的几种刻画,进一步得到$\overline{[T,T]}$是$T$的理想.

英文摘要:

      Let $T$ be an associative algebra over the complex filed, and the commutator $[T, T]$ of $T$ be the linear span of the set $\{[a,b]:a,b\in T\}$. We describe the $\sigma-wot $ closure of the commutator of a nest algebra and the norm closure of the commutator of an TAF algebra.