Dvoretzky's theorem for operator spaces - Texas A&M University (TAMU) Scholar

We prove a version of Dvoretzky's theorem for operator spaces. Equivalently, we prove that any infinite dimensional operator space has an ultrapower containing completely isometrically a Hilbertian homogeneous operator space. As an application, we prove a version of the Lindenstrauss-Tzafriri complemented subspace theorem for operator spaces: if every closed subspace of an operator space E is completely boundedly complemented, then E is completely isomorphic to a Hilbertian homogeneous operator space.

Dvoretzky's theorem for operator spaces Academic Article