Turkish Journal of Mathematics
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,... .
DOI
10.3906/mat-1101-89
Keywords
Bergman space, multiplication operators, hyper-reflexive operator, commutant, hyper-invariant
First Page
483
Last Page
489
Recommended Citation
AHMADI, M. F, & HEDAYATIAN, K (2013). Commutants and hyper-reflexivity of multiplication operators. Turkish Journal of Mathematics 37 (3): 483-489. https://doi.org/10.3906/mat-1101-89
