  The paper deals with the distribution of eigenvalues of the compact fractal
pseudodifferential operator $T^\mu_\tau$, \[ \big( T^\mu_\tau f\big)(x) =
\int_{\mathbb{R}^n} e^{-ix\xi} \, \tau(x,\xi) \, \big( f\mu \big)^\vee (\xi) \,
\mathrm{d} \xi, \qquad x\in \mathbb{R}^n, \] in suitable special Besov spaces
$B^s_p (\mathbb{R}^n) = B^s_{p,p} (\mathbb{R}^n)$, $s>0$, $1<p<\infty$. Here
$\tau(x,\xi)$ are the symbols of (smooth) pseudodifferential operators
belonging to appropriate H\"{o}rmander classes $\Psi^\sigma_{1, \varrho}
(\mathbb{R}^n)$, $\sigma <0$, $0 \le \varrho \le 1$ (including the exotic case
$\varrho =1$) whereas $\mu$ is the Hausdorff measure of a compact $d$-set
$\Gamma$ in $\mathbb{R}^n$, $0<d<n$. This extends previous assertions for the
positive-definite selfadjoint fractal differential operator $(\mathrm{id} -
\Delta)^{\sigma/2} \mu$ based on Hilbert space arguments in the context of
suitable Sobolev spaces $H^s (\mathbb{R}^n) = B^s_2 (\mathbb{R}^n)$. We collect
the outcome in the {Main Theorem} below. Proofs are based on estimates for the
entropy numbers of the compact trace operator \[ \mathrm{tr}_\mu: \quad B^s_p
(\mathbb{R}^n) \hookrightarrow L_p (\Gamma, \mu), \quad s>0, \quad 1<p<\infty.
\] We add at the end of the paper a few personal reminiscences illuminating the
role of Pietsch in connection with the creation of approximation numbers and
entropy numbers.
