论文标题
希尔伯特空间对的c*-corresports的表示
Representations of C*-correspondences on pairs of Hilbert spaces
论文作者
论文摘要
我们研究了希尔伯特（Hilbert）空间成对的希尔伯特·比模型的表示。如果$ a $是a c*-algebra，$ \ mathsf {x} $是右hilbert $ a $ module，我们使用此类表示忠实地表示C*-Algebras $ \ Mathcal {k} _a _a _a（\ mathsf {x}} $ and $ \ m rathcal {$} $ a（\ l} _A（\ \ \ \）然后，我们扩展了该理论，以定义一对希尔伯特空间的$（a，b）$ c*corresporces的表示形式，并显示如何从$ b $的任何非等级表示。作为此类表示形式的应用，我们在$（a，b）$ c*-correspendence上提供了必要和充分的条件，以接纳Hilbert $ a $ a $ -b $ b $ -bimodule结构。最后，我们展示了如何表示两个c*correspendence的内部张量产物。
We study representations of Hilbert bimodules on pairs of Hilbert spaces. If $A$ is a C*-algebra and $\mathsf{X}$ is a right Hilbert $A$-module, we use such representations to faithfully represent the C*-algebras $\mathcal{K}_A(\mathsf{X})$ and $\mathcal{L}_A(\mathsf{X})$. We then extend this theory to define representations of $(A,B)$ C*-correspondences on a pair of Hilbert spaces and show how these can be obtained from any nondegenerate representation of $B$. As an application of such representations, we give necessary and sufficient conditions on an $(A,B)$ C*-correspondences to admit a Hilbert $A$-$B$-bimodule structure. Finally, we show how to represent the interior tensor product of two C*-correspondences.
