For every proposed constants a,b≥1, some origin-symmetric convex body K in a finite dimension violates Pietsch’s proposed dimension-free covering-entropy comparison with the cube: log N(K,B∞)>b log N(B∞°,a⁻¹K°).
For every proposed constants a,b≥1, some origin-symmetric convex body K in a finite dimension violates Pietsch’s proposed dimension-free covering-entropy comparison with the cube: log N(K,B∞)>b log N(B∞°,a⁻¹K°).
For every proposed constants a,b≥1, some origin-symmetric convex body K in a finite dimension violates Pietsch’s proposed dimension-free covering-entropy comparison with the cube: log N(K,B∞)>b log N(B∞°,a⁻¹K°).
If correct, disproves the universal metric-entropy duality conjecture even with a cube as the covering body.
Do dimension-free covering-entropy duality constants exist for all symmetric convex bodies?
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