Title of article :
Commutants and hyper-reflexivity of multiplication operators
Author/Authors :
FAGHIH-AHMADI, Masoumeh shiraz university - College of Sciences - Department of Mathematics, شيراز, ايران , HEDAYATIAN, Karim shiraz university - College of Sciences - Department of Mathematics, شيراز, ايران
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 varphi (z) = z^k, k=1, 2,... .
Keywords :
Bergman space , multiplication operators , hyper , reflexive operator , commutant , hyper , invariant
Journal title :
Turkish Journal of Mathematics
Journal title :
Turkish Journal of Mathematics