On quasi-affinity and reducing subspaces of multiplication operator on a certain closed subspace

Authors

YUCHENG LI
LINA SONG
WENHUA LAN

DOI

10.3906/mat-2001-43

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 $H$.

Keywords

Bergman space, multiplication operator, quasi-affinity, reducing subspaces

First Page

1534

Last Page

1543

Recommended Citation

LI, YUCHENG; SONG, LINA; and LAN, WENHUA (2020) "On quasi-affinity and reducing subspaces of multiplication operator on a certain closed subspace," Turkish Journal of Mathematics: Vol. 44: No. 5, Article 2. https://doi.org/10.3906/mat-2001-43
Available at: https://journals.tubitak.gov.tr/math/vol44/iss5/2