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arXiv · 1306.3411

Bilinear Ideals in Operator Spaces

Verónica Dimant·Maite Fernández-Unzueta
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Abstract

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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Verónica Dimant, Maite Fernández-Unzueta. 2015-03-26. Bilinear Ideals in Operator Spaces. https://arxiv.org/abs/1306.3411

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