In the first section of this paper the relationship between quasiaffine invertibility and invertibility of operators is investigated.For example,
it is proved that if T is paranormal and has a right quasiaffine inverse,
then T is invertible.In§2,several properties of operators which is inhe-
rited by quasiaffine transforms(or right quasiaffine inverses)are given.
In§3,the existence problem about the invariant subspaces of operators is
discussed and some sufflicient conditions in terms of properties of quasia-
ffine transforms of operators are obtained.