%0 Journal Article
%T Bilinear Ideals in Operator Spaces
%A Ver¨Žnica Dimant
%A Maite Fern¨˘ndez-Unzueta
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1306.3411v3