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Israel Journal of Mathematics

, Volume 9, Issue 4, pp 488–506 | Cite as

On bases, finite dimensional decompositions and weaker structures in Banach spaces

  • W. B. Johnson
  • H. P. Rosenthal
  • M. Zippin
Article

Abstract

This is an investigation of the connections between bases and weaker structures in Banach spaces and their duals. It is proved, e.g., thatX has a basis ifX* does, and that ifX has a basis, thenX* has a basis provided thatX* is separable and satisfies Grothendieck’s approximation property; analogous results are obtained concerning π-structures and finite dimensional Schauder decompositions. The basic results are then applied to show that every separable p space has a basis.

Keywords

Banach Space Approximation Property Natural Projection Separable Banach Space Invertible Operator 
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

© The Weizmann Science Press of Israel 1971

Authors and Affiliations

  • W. B. Johnson
    • 1
    • 2
  • H. P. Rosenthal
    • 1
    • 2
  • M. Zippin
    • 1
    • 2
  1. 1.University of HoustonHouston
  2. 2.University of CaliforniaBerkeley

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