We expand upon work from many hands on the decomposition of nuclear maps. Such maps can be characterised by their ability to be approximately written as the composition of maps to and from matrices. Under certain conditions (such as quasidiagonality), we can find a decomposition whose maps behave nicely, by preserving multiplication up to an arbitrary degree of accuracy and being constructed from order-zero maps (as in the definition of nuclear dimension). We investigate these conditions and relate them to a W*-analogue.

中文翻译：

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核图的近似乘法分解

我们扩展了许多人对核图分解的工作。这种映射的特征在于它们能够被近似地写为映射到矩阵和从矩阵映射的组合。在某些条件下（例如准对角性），我们可以通过将乘法保持到任意精度并从零阶映射（如核维数的定义中）构造来找到其映射表现良好的分解。我们调查这些条件并将它们与 W* 类似物联系起来。