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Israel Journal of Mathematics

, Volume 13, Issue 3–4, pp 301–310 | Cite as

A complementary universal conjugate Banach space and its relation to the approximation problem

  • William B. Johnson
Article

Abstract

LetC 1=(ΣG n ) l 1, where (G n ) is a sequence which is dense (in the Banach-Mazur sense) in the class of all finite dimensional Banach spaces. IfX is a separable Banach space, thenX * is isometric to a subspace ofC 1 * =(ΣG n * ) m which is the range of a contractive projection onC 1 * . Separable Banach spaces whose conjugates are isomorphic toC 1 * are classified as those spaces which contain complemented copies of C1. Applications are that every Banach space has the [metric] approximation property ([m.] a.p., in short) iff (ΣG n * ) m does, and if there is a space failing the m.a.p., thenC 1 can be equivalently normed to fail the m.a.p.

Keywords

Banach Space Equivalent Norm Studia Math Separable Banach Space Unconditional Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1972

Authors and Affiliations

  • William B. Johnson
    • 1
  1. 1.Ohio State UniversityColumbus

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