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Symmetric block bases in finite-dimensional normed spaces

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Abstract

It is shown that for 1 ≦p < ∞, any basisC-equivalent to the unit vector basis ofl n p has a (1 + ε)-symmetric block basis of cardinality proportional ton/logn. When 1 <p < ∞, an upper bound proportional ton log logn/logn is also obtained. These results extend results of Amir and Milman in [2].

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References

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  1. Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, CB2 1SD, Cambridge, England

    W. T. Gowers

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  1. W. T. Gowers
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Gowers, W.T. Symmetric block bases in finite-dimensional normed spaces. Israel J. Math. 68, 193–219 (1989). https://doi.org/10.1007/BF02772661

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  • DOI: https://doi.org/10.1007/BF02772661

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