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

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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 separableℒ p space has a basis.

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Authors and Affiliations

  1. University of Houston, Houston, Texas

    W. B. Johnson, H. P. Rosenthal & M. Zippin

  2. University of California, Berkeley, California

    W. B. Johnson, H. P. Rosenthal & M. Zippin

Authors
  1. W. B. Johnson
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  2. H. P. Rosenthal
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  3. M. Zippin
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Additional information

The second and third named authors have been supported by the NSF Grant GP 12997.

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Johnson, W.B., Rosenthal, H.P. & Zippin, M. On bases, finite dimensional decompositions and weaker structures in Banach spaces. Israel J. Math. 9, 488–506 (1971). https://doi.org/10.1007/BF02771464

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  • DOI: https://doi.org/10.1007/BF02771464

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