[Banach] Abstract of a paper by S. Artstein, V. Milman, and S. J. Szarek
alspach at www.math.okstate.edu
Thu Jul 15 07:10:59 CDT 2004
This is an announcement for the paper "Duality of metric entropy" by
S. Artstein, V. Milman, and S. J. Szarek.
Abstract: For two convex bodies K and T in $R^n$, the covering number of K
by T, denoted N(K,T), is defined as the minimal number of translates of T
needed to cover K. Let us denote by $K^o$ the polar body of K and by D the
euclidean unit ball in $R^n$. We prove that the two functions of t, N(K,tD)
and N(D, tK^o), are equivalent in the appropriate sense, uniformly
over symmetric convex bodies K in $R^n$ and over positive integers n. In
particular, this verifies the duality conjecture for entropy numbers
of linear operators, posed by Pietsch in 1972, in the central case when
either the domain or the range of the operator is a Hilbert space.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 46B10; 47A05; 52C17; 51F99
Remarks: 17 p., LATEX
The source file(s), ArtMilSzaAoM.tex: 40692 bytes, is(are) stored in
gzipped form as 0407236.gz with size 14kb. The corresponding postcript
file has gzipped size 68kb.
Submitted from: szarek at cwru.edu
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