论文标题
弱$ a $ frames和弱$ a $ -semi-frames
Weak $A$-frames and weak $A$-semi-frames
论文作者
论文摘要
在回顾了帧和下半框架之间的相互作用之后，我们介绍了由密集定义的运算符$ a $ $ a $或简称\ emph {弱$ a $ a $ a $ -semi-frame}控制的下半框架的概念，我们研究了其属性。特别是，我们将其与\ cite {gb}中引入的下部原子系统的较低原子系统进行了比较。我们讨论二元性属性，并提出了一些弱$ $ upper半框架的可能定义。提出了具体的例子。
After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator $A$ or, for short, a \emph{weak lower $A$-semi-frame} and we study its properties. In particular, we compare it with that of lower atomic systems, introduced in \cite{GB}. We discuss duality properties and we suggest several possible definitions for weak $A$-upper semi-frames. Concrete examples are presented.
