Complemented subspaces of spaces obtained by interpolation

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If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A₀,A₁) such that A₀ and A₁ are isometric to X⊕ V, and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z. Thus many properties of Banach spaces, including having non-trivial cotype, having the Radon-Nikodym property, and having the analytic unconditional martingale difference sequence property, do not pass to intermediate spaces.