  Weighted shift operators $B$ in space $L^2(X,\mu)$ that are induced by
Morse-Smale type of mappings are considered. A description of the properties of
$B-\lambda I$ for $\lambda$ belonging to spectrum $\Sigma(B)$ is given. In
particular, there is the necessary and sufficient condition that $B-\lambda I$
be a one-sided invertible and the condition that set $Im(B-\lambda I)$ be
non-closed. These conditions use a new notation: an oriented decomposition of
oriented graph $G(X,\alpha)$ generated by mapping $\alpha$
