Commutants and hyper-reflexivity of multiplication operators

Authors : Masoumeh FAGHIH-AHMADI, Karim HEDAYATIAN

Pages : 483-489

Doi:10.3906/mat-1101-89

View : 10 | Download : 9

Publication Date : 0000-00-00

Article Type : Research Paper

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 insert ignore into journalissuearticles values(z); = zk, k=1, 2,... .
Keywords : Bergman space, multiplication operators, hyper reflexive operator, commutant, hyper invariant