Complemented subspaces of spaces obtained by interpolation

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Complemented subspaces of spaces obtained by interpolation

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/9822

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Title: Complemented subspaces of spaces obtained by interpolation
Author: Montgomery-Smith, Stephen, 1963-; Garling, D. J. H.
Date: 2011-01-31
Abstract: 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.
URI: http://hdl.handle.net/10355/9822

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