Structural representation of inverse operator in Banach space

The problem of construction of inverse operator for the equation $Az=u$ ($u\in U$, $z\in F$; $U$, $F$ are metric spaces) is considered. The algorithm for solving the inverse problems based on structural representation of inverse operators as periodic structure is suggested. The necessary and sufficient conditions of fundamentality of periodic structure are formulated. It is shown that if these conditions are fulfilled the periodic structure operator converges to the inverse operator.