Hyperplane conjecture for quotient spaces of $L_p$

Marius Junge

Hyperplane conjecture for quotient spaces of $L_p$

Functional Analysis 2008-02-03 v1

Authors: Marius Junge

Abstract

We give a positive solution for the hyperplane conjecture of quotient spaces F of $L_p$ , where $1<p\kll\infty$ . $vol(B_F)^{\frac{n-1}{n}} \kl c_0 \pl p' \pl \sup_{H \p hyperplane} vol(B_F\cap H) \pl.$ This result is extended to Banach lattices which does not contain $\ell_1^n$ 's uniformly. Our main tools are tensor products and minimal volume ratio with respect to $L_p$ -sections.

Keywords

lp spaces and inequalities banach spaces conjectures and proofs

Cite

@article{arxiv.math/9312207,
  title  = {Hyperplane conjecture for quotient spaces of $L_p$},
  author = {Marius Junge},
  journal= {arXiv preprint arXiv:math/9312207},
  year   = {2008}
}

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