This is an announcement for the paper "Subspace structure of some operator and Banach spaces" by Timur Oikhberg and Christian Rosendal. Abstract: We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete $\ks$. We also investigate some interesting properties of completely unconditional bases of the spaces from this family. In the Banach space setting, we construct a space for which the relation of isometry of subspaces is equivalent to equality of real numbers. Archive classification: math.FA math.LO Remarks: 30 pages Submitted from: toikhber@math.uci.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.3591 or http://arXiv.org/abs/1009.3591