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ArticleOriginal scientific text

Title

Volume ratios in Lp-spaces

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, Technion, Haifa 32000, Israel
  2. Math. Seminar Kiel, Ludewig Meyn Str.4, 24098 Kiel, Germany
  3. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.

Abstract

There exists an absolute constant c0 such that for any n-dimensional Banach space E there exists a k-dimensional subspace F ⊂ E with k≤ n/2 such that infellipsoid ɛ⊂BE(vol(BE)vol(ε))1/n≤c0infzonoid Z⊂BF(vol(BF)vol(Z))1/k. The concept of volume ratio with respect to ℓp-spaces is used to prove the following distance estimate for 2≤q≤p<∞: supF⊂ℓp,dimF=ninfG⊂Lq,dimG=nd(F,G)∼cpqn(q/2)(1/q-1/p).

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Studia Mathematica
1999/136/2
Export to PBN, Opens in new tab
Pages:
147-182
Main language of publication
English
Received
1998-09-04
Accepted
1999-03-05
Published
1999
Exact and natural sciences