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Copies of l n p ’s uniformly in the spaces Π2(C[0, 1],X) and Π1(C[0, 1],X)

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Abstract

We study the presence of copies of l n p ’s uniformly in the spaces Π2(C[0, 1],X) and Π1(C[0, 1],X). By using Dvoretzky’s theorem we deduce that if X is an infinite-dimensional Banach space, then Π2(C[0, 1],X) contains \(\lambda \sqrt 2 \) -uniformly copies of l n∞ ’s and Π1(C[0, 1],X) contains λ-uniformly copies of l n2 ’s for all λ > 1. As an application, we show that if X is an infinite-dimensional Banach space then the spaces Π2(C[0, 1],X) and Π1(C[0, 1],X) are distinct, extending the well-known result that the spaces Π2(C[0, 1],X) and N(C[0, 1],X) are distinct.

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  1. Department of Mathematics, Ovidius University of Constanţa, Bd. Mamaia 124, 900527, Constanţa, Romania

    Dumitru Popa

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  1. Dumitru Popa
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Popa, D. Copies of l n p ’s uniformly in the spaces Π2(C[0, 1],X) and Π1(C[0, 1],X). Czech Math J 67, 457–467 (2017). https://doi.org/10.21136/CMJ.2017.0009-16

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  • DOI: https://doi.org/10.21136/CMJ.2017.0009-16

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