Assume that $X$ is a Banach space in which every Hilbertian subspace is complemented (let's say that all the projections are uniformly bounded). What can we say about $X$? It has to be K-convex. By Maurey's extension theorem, this property holds for all spaces of type 2, so we cannot say more. But do we have something more than K-convexity in general?
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