  We investigate pointwise convergence of entangled ergodic averages of
Dunford-Schwartz operators $T_0,T_1,\ldots, T_m$ on a Borel probability space.
These averages take the form \[ \frac{1}{N^k}\sum_{1\leq n_1,\ldots, n_k\leq N}
T_m^{n_{\alpha(m)}}A_{m-1}T^{n_{\alpha(m-1)}}_{m-1}\ldots
A_2T_2^{n_{\alpha(2)}}A_1T_1^{n_{\alpha(1)}} f, \] where $f\in L^p(X,\mu)$ for
some $1\leq p<\infty$, and
$\alpha:\left\{1,\ldots,m\right\}\to\left\{1,\ldots,k\right\}$ encodes the
entanglement. We prove that under some joint boundedness and twisted
compactness conditions on the pairs $(A_i,T_i)$, almost everywhere convergence
holds for all $f\in L^p$. We also present an extension to polynomial powers in
the case $p=2$, in addition to a continuous version concerning Dunford-Schwartz
$C_0$-semigroups.
