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Weakly null sequences in  |
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| Authors: | William B. Johnson Bernard Maurey Gideon Schechtman |
| Affiliation: | Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368 ; Laboratoire d'Analyse et de Mathématiques Appliquées, UMR CNRS 8050, Université de Marne la Vallée, 77454 Champs-sur-Marne, France ; Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel |
| Abstract: | We construct a weakly null normalized sequence  in  so that for each  , the Haar basis is  -equivalent to a block basis of every subsequence of  . In particular, the sequence  has no unconditionally basic subsequence. This answers a question raised by Bernard Maurey and H. P. Rosenthal in 1977. A similar example is given in an appropriate class of rearrangement invariant function spaces. |
| Keywords: | $L_1$ Haar basis unconditional basic sequence weakly null. |
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