  We compare the Kolmogorov and entropy numbers of compact operators mapping
from a Hilbert space into a Banach space. We then apply these general findings
to embeddings between reproducing kernel Hilbert spaces and $L_\infty(\mu)$.
Here we provide a sufficient condition for a gap of the order $n^{1/2}$ between
the associated interpolation and Kolmogorov $n$-widths. Finally, we show that
in the multi-dimensional Sobolev case, this gap actually occurs between the
Kolmogorov and approximation widths.
