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Weak Distances between Random Subproportional Quotients of $\ell^m_1$

Volume 60 / 2012

Piotr Mankiewicz Bulletin Polish Acad. Sci. Math. 60 (2012), 285-294 MSC: 46B09, 46B20. DOI: 10.4064/ba60-3-8


Lower estimates for weak distances between finite-dimensional Banach spaces of the same dimension are investigated. It is proved that the weak distance between a random pair of $n$-dimensional quotients of $\ell^{n^2}_1$ is greater than or equal to $c\sqrt{n/\log^3 n}$.


  • Piotr MankiewiczInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    P.O. Box 21
    00-956 Warszawa 10, Poland

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