[Banach] Abstract of a paper by S. Artstein, V. Milman, S. J. Szarek, and N. Tomczak-Jaegermann

[Dale Alspach]

This is an announcement for the paper "On convexified packing
and entropy duality" by S. Artstein, V. Milman, S. J. Szarek, and
N. Tomczak-Jaegermann.


Abstract: For a compact operator acting between two Banach spaces,
a 1972 duality conjecture due to Pietsch asserts that its entropy
numbers and those of its adjoint are equivalent. This is equivalent
to a dimension-free inequality relating covering (or packing) numbers
for convex bodies to those of their polars. The duality conjecture has
been recently proved (see math.FA/0407236) in the central case when one
of the Banach spaces is Hilbertian, which - in the geometric setting -
corresponds to a duality result for symmetric convex bodies in Euclidean
spaces. In the present paper we define a new notion of "convexified
packing," show a duality theorem for that notion, and use it to prove the
duality conjecture under much milder conditions on the spaces involved
(namely, that one of them is K-convex).

Archive classification: Functional Analysis; Metric Geometry

Mathematics Subject Classification: 46B10; 46B07; 46B50; 47A05; 52C17;
51F99

Remarks: 6 p., LATEX

The source file(s), ConvPackShort5.tex: 21620 bytes, is(are) stored in
gzipped form as 0407238.gz with size 8kb. The corresponding postcript
file has gzipped size 43kb.

Submitted from: szarek at cwru.edu

The paper may be downloaded from the archive by web browser from URL

 http://front.math.ucdavis.edu/math.FA/0407238

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 http://arXiv.org/abs/math.FA/0407238

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