### On quasi-compactness of operator nets on Banach spaces

The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Räbiger net ${\left({T}_{\lambda}\right)}_{\lambda}$ is equivalent to quasi-compactness of some operator ${T}_{\lambda}$. We prove that strong convergence of a quasi-compact uniform Lotz-Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.