We introduce the notion of $\Delta$ and $\sigma\,\Delta-$ pairs for operator algebras and characterise $\Delta-$ pairs through their categories of left operator modules over these algebras. Furthermore, we introduce the notion of $\Delta$-Morita equivalent operator spaces and prove a similar theorem about their algebraic extensions. We prove that $\sigma\Delta$-Morita equivalent operator spaces are stably isomorphic and vice versa. Finally, we study unital operator spaces, emphasising their left (resp. right) multiplier algebras, and prove theorems that refer to $\Delta$-Morita equivalence of their algebraic extensions.

中文翻译：

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希尔伯特空间上算子的代数和空间的 Morita 刻画

我们为算子代数引入了 $\Delta$ 和 $\sigma\,\Delta-$ 对的概念，并通过它们在这些代数上的左算子模块的类别来表征 $\Delta-$ 对。此外，我们引入了 $\Delta$-Morita 等价算子空间的概念，并证明了关于它们的代数扩展的类似定理。我们证明 $\sigma\Delta$-Morita 等价算子空间是稳定同构的，反之亦然。最后，我们研究了单位算子空间，强调了它们的左（右）乘数代数，并证明了引用它们代数扩展的 $\Delta$-Morita 等价的定理。