In the first section of this paper the relationship between quasiaffine invertibility and invertibility of operators is investigated. For examples 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 inherited 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 quasiaffine transforms of operators are obtained.
Let T be pure subnormal operator. In this paper necessary and sufficiert conditions that T=N+K are given,where N is normal, K is quasinormal and NK=KN.
