  $K$-frames and atomic systems for an operator $K$ in Hilbert spaces were
introduced by Gavruta \cite{12} and further studied by Xio, Zhu and Gavruta
\cite{21}. In this paper, we have introduced the notion of an approximative
atomic system for an operator $K$ in Banach spaces and obtained interesting
results. A complete characterization of family of approximative local atoms of
subspace of Banach space has been obtained. Also, a necessary and sufficient
condition for the existence of an approximative atomic system for an operator
$K$ is given. Finally, explicit methods are given for the construction of an
approximative atomic systems for an operator $K$ from a given Bessel sequence
and approximative $\mathcal{X}_d$-Bessel sequence.
