Asymptotic reflexivity
- 作者：Hassan Yousefi
- 关键词：Algebraic reflexivity ; Approximate reflexivity
- 刊名：Linear Algebra and its Applications
- 出版年：2007
- 期刊代码：38_00243795
- 类别：mt
- 出版时间：15 April 2007
- 卷：422
- 期：2-3
- 页码：604-615
- 文件大小：178 K
摘要
We introduce a new version of reflexivity, akin to approximate reflexivity, called Asymptotic Reflexivity. We prove that the unital algebra generated by any operator in , where is a Hilbert space, is asymptotically reflexive. We also show that a linear subspace of is asymptotically reflexive if and only if is asymptotically, where is the set of finite rank operators in . This result, in particular, implies that the space is asymptotically reflexive. An analogous version of Loginov–Shulman Theorem will be also proved for this notion of reflexivity. This result, in particular, implies that any linear subspace of normal operators is asymptotically reflexive. The relation between this notion of reflexivity and completely rank-nonincreasing maps will be studied as well.