Weak forms of supercyclity and a class of paranormal operators

Sungeun Jung, Insook Kim, Eungil Ko
2014 Mathematical Inequalities & Applications  
In this paper, we give several properties of class A operators, an interesting subclass of paranormal operators. In particular, we consider the operators T ∈ L (H ) such that T − λ is a class A operator for every λ ∈ C . We also provide some cases for class A operators to have a nontrivial invariant subspace. Finally, we prove that there are no N -supercyclic class A operators with trivial kernel for any positive integer N and that weakly supercyclic class A operators with trivial kernel must
more » ... normal. (2010) : 47B20, 47A16. Mathematics subject classification
doi:10.7153/mia-17-61 fatcat:hqrgfjdjavhvxnvppsx4v2ykqm