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A nonreflexive Banach space that is uniformly nonoctahedral

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Abstract

An example is given of a nonreflexive Banach space\(\tilde X\) that is uniformly nonoctahedral (or uniformly non-l (3)1 ), in the sense that there is a λ>1 such that there is no isomorphismT ofl (3)1 into\(\tilde X\) for which

$$\lambda ^{ - 1} \left\| x \right\|\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } \left\| {T(x)} \right\|\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } \lambda \left\| x \right\|{\text{ }}if x \in l_1^{(3)}$$

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Authors and Affiliations

  1. Department of Mathematics, Claremont Graduate School, Claremont, California, U. S. A.

    Robert C. James

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  1. Robert C. James
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Additional information

This research was supported in part by NSF Grant GP-28578. It was presented in preliminary form at a conference at Oberwolfach, Germany, October 15–20, 1973.

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James, R.C. A nonreflexive Banach space that is uniformly nonoctahedral. Israel J. Math. 18, 145–155 (1974). https://doi.org/10.1007/BF02756869

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  • DOI: https://doi.org/10.1007/BF02756869

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