66 citations · 66 across the 5 of their papers we have counts for
6 papers
On convexified packing and entropy duality
S. Artstein, V. Milman, S. J. Szarek +1
A 1972 duality conjecture due to Pietsch asserts that the entropy numbers of a compact operator acting between two Banach spaces and those of its adjoint are (in an appropriate sen…
Duality of metric entropy
S. Artstein, V. Milman, S. J. Szarek
For two convex bodies K and T in , 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 …
Saturating Constructions for Normed Spaces II
Stanislaw J. Szarek, Nicole Tomczak-Jaegermann
We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property…
Saturating Constructions for Normed Spaces
Stanislaw J. Szarek, Nicole Tomczak-Jaegermann
We prove several results of the following type: given finite dimensional normed space V there exists another space X with log (dim X) = O(log (dim V)) and such that every subspace…
The volume of separable states is super-doubly-exponentially small
Stanislaw Szarek
In this note we give sharp estimates on the volume of the set of separable states on N qubits. In particular, the magnitude of the "effective radius" of that set in the sense of vo…
A Characterization of Completely-Positive Trace-Preserving Maps on 2x2 Matrices
M. B. Ruskai, E. Werner, S. Szarek
This paper has been superseded by quant-ph/0101003.