D.J.H. Garling and Stephen Montgomery-Smith, Complemented subspaces of spaces obtained by interpolation. J. L.M.S. (2) 44 (1991), 503-513. 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 \((A_0,A_1)\) such that \(A_0\) and \(A_1\) are isometric to \(X\oplus V\), 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. (tex, dvi, ps, pdf.)

 

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