Volume ratios in $L_p$-spaces

Gordon, Yehoram; Junge, Marius

Volume ratios in

L_{p}

-spaces

Gordon, Yehoram ; Junge, Marius

Studia Mathematica, Tome 133 (1999), p. 147-182 / Harvested from The Polish Digital Mathematics Library

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Résumé

There exists an absolute constant $c_{0}$ such that for any n-dimensional Banach space E there exists a k-dimensional subspace F ⊂ E with k≤ n/2 such that $i n f_{e l l i p s o i d ε \subset B_{E}} {(v o l (B_{E}) / v o l (ε))}^{1 / n} \leq c_{0} i n f_{z o n o i d Z \subset B_{F}} {(v o l (B_{F}) / v o l (Z))}^{1 / k}$ . The concept of volume ratio with respect to $ℓ_{p}$ -spaces is used to prove the following distance estimate for $2 \leq q \leq p < \infty$ : $s u p_{F \subset ℓ_{p}, d i m F = n} i n f_{G \subset L_{q}, d i m G = n} d (F, G) \sim_{c_{p q}} n^{(q / 2) (1 / q - 1 / p)}$ .

Publié le : 1999-01-01

Zbl 0952.46008

EUDML-ID : urn:eudml:doc:216665

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     author = {Yehoram Gordon and Marius Junge},
     title = {Volume ratios in $L\_p$-spaces},
     journal = {Studia Mathematica},
     volume = {133},
     year = {1999},
     pages = {147-182},
     zbl = {0952.46008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv136i2p147bwm}
}

Gordon, Yehoram; Junge, Marius. Volume ratios in $L_p$-spaces. Studia Mathematica, Tome 133 (1999) pp. 147-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv136i2p147bwm/

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