Complemented Subspaces of Spaces Obtained by Interpolation

Type: Article

Publication Date: 1991-12-01

Citations: 15

DOI: https://doi.org/10.1112/jlms/s2-44.3.503

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.

Locations

  • Journal of the London Mathematical Society - View
  • MOspace Institutional Repository (University of Missouri) - View - PDF

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