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Proceedings of the American Mathematical Society

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Embedding $ l\sb{p}\sp{n\sp{\alpha }}$ in $ l\sp{n}\sb{p,q}$


Authors: N. L. Carothers and P. H. Flinn
Journal: Proc. Amer. Math. Soc. 88 (1983), 523-526
MSC: Primary 46B15; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9939-1983-0699425-9
MathSciNet review: 699425
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Abstract: It is shown that for $ 1 < p < \infty $, $ 1 \leqslant q \leqslant \infty $ and $ 0 < \alpha < 1$, there is a constant $ C = C(p,q,\alpha ) < \infty $ such that $ l_p^k$ is $ C$-isomorphic to a subspace of $ l_{p,q}^n$ where $ k = O({n^\alpha })$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0699425-9
Keywords: Lorentz sequence space, basic sequence
Article copyright: © Copyright 1983 American Mathematical Society

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