Abstract
It is proved that the Banach spacel p with 1≦p<2 contains a subspace without AP (the case 2<p≦∞ follows from the Enflo’s construction and also from the present one). The result generalizes to the following one: if the supremum of types ofX is strictly less than 2 or if the infimum of cotypes ofX is strictly more than 2 thenX contains a subspace without AP.
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References
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Szankowski, A. Subspaces without the approximation property. Israel J. Math. 30, 123–129 (1978). https://doi.org/10.1007/BF02760833
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DOI: https://doi.org/10.1007/BF02760833