In this paper, we introduce the notion of abstract local operator algebras and operator modules, and provide a representation theorem for them which extends the BRS theorem for operator algebras. Furthermore, we give a new proof for the representation theorem of local operator systems. Also, we investigate the Haagerup tensor product of local operator spaces and Morita equivalence of local operator algebras.

中文翻译：

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无界算子代数

在本文中，我们介绍了抽象局部算子代数和算子模块的概念，并为它们提供了表示定理，从而扩展了算子代数的BRS定理。此外，我们为局部算子系统的表示定理提供了新的证明。此外，我们研究了局部算子空间的Haagerup张量积和局部算子代数的Morita等价。