Volumetric invariants and operators on random families of Banach spaces
Piotr Mankiewicz ; Nicole Tomczak-Jaegermann
Studia Mathematica, Tome 157 (2003), p. 315-335 / Harvested from The Polish Digital Mathematics Library
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The geometry of random projections of centrally symmetric convex bodies in ℝN is studied. It is shown that if for such a body K the Euclidean ball B₂N is the ellipsoid of minimal volume containing it and a random n-dimensional projection B=PH(K) is “far” from PH(B₂N) then the (random) body B is as “rigid” as its “distance” to PH(B₂N) permits. The result holds for the full range of dimensions 1 ≤ n ≤ λN, for arbitrary λ ∈ (0,1).

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:285217 
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Piotr Mankiewicz; Nicole Tomczak-Jaegermann. Volumetric invariants and operators on random families of Banach spaces. Studia Mathematica, Tome 157 (2003) pp. 315-335. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-2-10/