Turkish Journal of Mathematics
Abstract
Let $H$ denote a certain closed subspace of the Bergman space $A_{\alpha}^{2}({\B}_{n})(\alpha>-1)$ of the unit ball in $\mathbb{C}^{n}$. In this paper, we prove that the operator $\bigoplus\limits_{1}^{m}M_{z^{(s_{1},\cdots,s_{n})}}$ is quasi-affine to the multiplication operator $M_{z^{(ms_{1},\cdot\cdot\cdot,ms_{n})}}$ on $H$. Furthermore, the reducing subspaces of $M_{z^{(ms_{1},\cdots,ms_{n})}}$ are characterized on $H$.
DOI
10.3906/mat-2001-43
Keywords
Bergman space, multiplication operator, quasi-affinity, reducing subspaces
First Page
1534
Last Page
1543
Recommended Citation
LI, Y, SONG, L, & LAN, W (2020). On quasi-affinity and reducing subspaces of multiplication operator on a certain closed subspace. Turkish Journal of Mathematics 44 (5): 1534-1543. https://doi.org/10.3906/mat-2001-43
