A short note on the comparison of interpolation widths, entropy numbers, and Kolmogorov widths

We compare the Kolmogorov and entropy numbers of compact operators mapping from a Hilbert space into a Banach space. These general findings are then applied to embeddings between reproducing kernel Hilbert spaces and L∞(μ). Here a sufficient condition for a gap of the order n1/2 between the associated interpolation and Kolmogorov n-widths is derived. Finally, we show that in the multi-dimensional Sobolev case, this gap actually occurs between the Kolmogorov and approximation widths.