On the composition of operators in vector spaces and their Noether property

Abstract

Under the minimal assumptions imposed on given spaces, the sufficient conditions are established, under which the composition $BA$ of operators $A$ and $B$ has the Noether property and is normally solvable. Similar conditions, guaranteeing that the operator $A$ is normally solvable or possesses the Noether property, are obtained for the operators $B$ and $AВ$ .