- Turkish Journal of Mathematics
- Vol: 37 Issue: 3
- Commutants and hyper-reflexivity of multiplication operators
Commutants and hyper-reflexivity of multiplication operators
Authors : Masoumeh Faghih-ahmadi, Karim Hedayatian
Pages : 483-489
Doi:10.3906/mat-1101-89
View : 11 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We characterize the commutants of some multiplication operators on a Banach space of analytic functions defined on a bounded domain in the plane. Under certain conditions on the symbol of a multiplication operator, we show that its commutant is a set of multiplication operators. This partially answers a question of Axler, Cuckovic and Rao. Next, the hyper-reflexivity of these multiplication operators are proved. The paper is concluded by proving the hyper-reflexivity of the multiplication operators with symbols j (z) = zk, k=1, 2,... .Keywords : Bergman space, multiplication operators, hyper-reflexive operator, commutant, hyper-invariant