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Complemented subspaces of spaces obtained by interpolation

D. J. H. Garling·Stephen J. Montgomery-Smith
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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 (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.

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BibTeXRIS

D. J. H. Garling, Stephen J. Montgomery-Smith. 1999-12-04. Complemented subspaces of spaces obtained by interpolation. https://arxiv.org/abs/math/9201212

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