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The nonlinear geometry of operator spaces has recently started to beinvestigated. Many notions of nonlinear embeddability have been introduced sofar, but, as noticed before by other authors, it was not clear whether theycould be considered ``correct notions''. The main goal of these notes is toprovide the missing evidence to support that \emph{almost complete coarseembeddability} is ``a correct notion''. This is done by proving results aboutthe complete isomorphic theory of $\ell_1$-sums of certain operators spaces.Several results on the complete isomorphic theory of $c_0$-sums of operatorspaces are also obtained.

Coarse geometry of operator spaces and complete isomorphic embeddings into $\ell_1$ and $c_0$-sums of operator spaces