  We prove an abstract theorem on keeping the compactness property of a linear
operator after interpolation in Banach spaces. No analytical presentation of
operators, spaces and interpolation functor is required. We use only some
little-known properties of compact sets and various facts about bases and basic
sequences (with detailed references to the monograph "Bases in Banach spaces",
Vol. I-II by I.M. Singer). Therefore the results are applicable to arbitrary
spaces and any interpolation functor, including the complex method. The
"two-sided" compactness is also mentioned at the end of this paper as a mere
corollary.
