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Onc 0 sequences in Banach spaces

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Abstract

A Banach space has property (S) if every normalized weakly null sequence contains a subsequences equivalent to the unit vector basis ofc 0. We show that the equivalence constant can be chosen “uniformly”, i.e., independent of the choice of the normalized weakly null sequence. Furthermore we show that a Banach space with property (S) has property (u). This solves in the negative the conjecture that a separable Banach space with property (u) not containingl 1 has a separable dual.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, 78712, Austin, TX, USA

    H. Knaust & E. Odell

Authors
  1. H. Knaust
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  2. E. Odell
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Additional information

This is part of this author's Ph.D. dissertation prepared at The University of Texas at Austin under the supervision of H. P. Rosenthal.

Research partially supported by NSF Grant DMS-8601752

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Knaust, H., Odell, E. Onc 0 sequences in Banach spaces. Israel J. Math. 67, 153–169 (1989). https://doi.org/10.1007/BF02937292

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  • DOI: https://doi.org/10.1007/BF02937292

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