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 \varphi (z) = z^k, k=1, 2,... .
Bergman space, multiplication operators, hyper-reflexive operator, commutant, hyper-invariant
AHMADI, MASOUMEH FAGHIH and HEDAYATIAN, KARIM
"Commutants and hyper-reflexivity of multiplication operators,"
Turkish Journal of Mathematics: Vol. 37:
3, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss3/11