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@cwru.edu
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