算子空间中的双线性理想
Bilinear Ideals in Operator Spaces
摘要：
引入了算子空间之间联合完全有界映射的双线性理想的概念。特别地，我们研究了完全核的双线性理想$\mathcal{N}$，完全积分的双线性理想$\mathcal{I }$，完全可扩双线性映射的双线性理想$\mathcal{E}$，$\mathcal{MB}$乘有界及其对称化$\mathcal{SMB}$.我们证明了它们的一些基本性质，其中之一是$\mathcal{I}$与内射算子空间张量积上的（线性）完全积分映射的理想自然一致.
英文摘要：
We introduce a concept of bilinear ideal of jointly completely bounded mappings between operator spaces. In particular, we study the bilinear ideals $\mathcal{N}$ of completely nuclear, $\mathcal{I }$ of completely integral, $\mathcal{E}$ of completely extendible bilinear mappings, $\mathcal{MB}$ multiplicatively bounded and its symmetrization $\mathcal{SMB}$. We prove some basic properties of them, one of which is the fact that $\mathcal{I}$ is naturally identified with the ideal of (linear) completely integral mappings on the injective operator space tensor product.
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