We explore connections between boundary representations of operator spaces and those of the associated Paulsen systems. Using the notions of finite representation and separating property which we introduce for operator spaces, the boundary representations for operator spaces are characterized. We also introduce weak boundary for operator spaces. Rectangular hyperrigidity for operator spaces introduced here is used to establish an analogue of Saskin’s theorem in the setting of operator spaces in finite dimensions.

中文翻译：

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边界表示和矩形超刚性

我们探索了运算符空间的边界表示与相关的Paulsen系统的边界表示之间的联系。利用我们为算子空间引入的有限表示和分离属性的概念，对算子空间的边界表示进行了刻画。我们还为运算符空间引入了弱边界。此处介绍的用于算子空间的矩形超刚度用于在有限维数下算子空间的设置中建立Saskin定理的类似物。