Abstract
A well known argument of James yields that if a Banach spaceX contains ℓ n1 ’s uniformly, thenX contains ℓ n1 ’s almost isometrically. In the first half of the paper we extend this idea to the ordinal ℓ1-indices of Bourgain. In the second half we use our results to calculate the ℓ1-index of certain Banach spaces. Furthermore we show that the ℓ1-index of a separable Banach space not containing ℓ1 must be of the form ωα for some countable ordinal α.
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Research supported by the NSF and TARP.
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Judd, R., Odell, E. Concerning Bourgain’s ℓ1-Index of a Banach space. Israel J. Math. 108, 145–171 (1998). https://doi.org/10.1007/BF02783046
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DOI: https://doi.org/10.1007/BF02783046