Reducibility of Invariant Subspaces of Operators Related to k-Quasiclass-A(n) Operators

作者：Yuan, Jiangtao^*; Wang, Caihong

来源：Complex Analysis and Operator Theory, 2016, 10(1): 153-169.

DOI：10.1007/s11785-015-0478-3

• Hyponormal operator
• Paranormal operator
• Class A(n)
• Invariant subspace
• Spectral continuity

It is well-known that hyponormal operators have many interesting properties, for example, if the restriction T | M of the hyponormal operator T on its nontrivial closed invariant subspace M is normal, then M reduces T. In order to discuss the reducibility of invariant subspaces of an operator, four properties of invariant subspaces (R-i, i = 1,..., 4) are introduced. Among others, it is proved that, for a k-quasi-A( n) operator T, if the restriction T | M is normal and injective, then M reduces T, thus the function s : T -. sigma(T) is continuous on the class of k-quasiclass-A(n) operators. Some examples related to class A(n) and n-paranormal operator are given which imply that the inclusion relations are strict.

• 出版日期2016-1
• 单位河南理工大学