Concerning the Bourgain `1 Index of a Banach Space

نویسندگان

  • ROBERT JUDD
  • EDWARD ODELL
چکیده

A well known argument of James yields that if a Banach space X contains `1 ’s uniformly, then X contains `1 ’s almost isometrically. In the first half of the paper we extend this idea to the ordinal `1-indices of Bourgain. In the second half we use our results to calculate the `1-index of certain Banach spaces. Furthermore we show that the `1-index of a separable Banach space not containing `1 must be of the form ω α for some countable ordinal α.

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تاریخ انتشار 2001