On the structure of subspaces of non-commutative \(L_p\)-spaces (Q2746840)

The authors study the structure of the subspaces of the spaces \(L_p({\mathcal A})\) associated with a (not necessarily semi-finite) von Neumann algebra \({\mathcal A}\). It is proved that if a subspace \(X\) contains uniformly the spaces \(S^n_p\) then it contains their \(\ell_p\) direct sum too and in the case \(p\geq 2\) it is extended to this frame the Kadec and Pełczynski dichotomy. Only sketch of proofs are given and as the authors say the missing details in the proofs will be supplied in a forthcoming paper.