可数生成子代数的自反性,分离向量和自反性

The Reflexivity of an Accountable Generated Algebra,Separate Vector and Reflexivity

设A是B(X,H)的可数生成子代数,本文验证了A在什么条件下是(拓扑)代数自反的,得到两个重要结论: 1、若AF=|0|,则A是(拓扑)代数自反的;2、若AF具有有限维支撑,则A是(拓扑)代数自反的充要条件是AF是(拓 扑)代教自反的。

A is an accountable generated algebra of B (X, H). We proved A is (topologically) algebraically reflexive under what condition. Two important results are obtained in this article. One is that if AF = {0}, then A is (topologically) algebraically reflexive. The other is that if the support of AF has definite dimension, then A is (topologically) algebraically reflexive if AF is (topologically) algebraically reflexive.