论文标题
算子代数的有限维近似值
Finite dimensional approximations in operator algebras
论文作者
论文摘要
如果非自动联合操作员代数将其嵌入矩阵代数的产物中，则据说是剩余的尺寸（RFD）。我们根据其矩阵状态空间来表征RFD运算符代数，此外，当且仅当每个表示每个表示都可以通过点弱操作员拓扑中的有限维数近似时，算子代数为rfd。这是EXEL定理的非自身辅助版本，并以$ C^*$ - 代数为代数。此外，我们构建了一个操作员代数的示例，该代数在该点上不可能在该点上进行近似值。结果，该操作员代数生成的最大$ c^*$ - 代数不是RFD。这回答了Clouâtre，Ramsey以及Clouâtre和Dor-On的问题。
A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD operator algebras in terms of their matrix state space, and moreover show that an operator algebra is RFD if and only if every representation can be approximated by finite dimensional ones in the point weak operator topology. This is a non-self-adjoint version of a theorem of Exel and Loring for $C^*$-algebras. Moreover, we construct an example of an operator algebra for which approximation in the point strong operator topology is not possible. As a consequence, the maximal $C^*$-algebra generated by this operator algebra is not RFD. This answers questions of Clouâtre and Ramsey and of Clouâtre and Dor-On.
