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 inver...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.展开更多
文摘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.
