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