On Similarity of Multiplication Operator on Weighted Bergman Space

Abstract

Let D be the unit disk and A 2 α (D) (α > −1) be the weighted Bergman space. In this paper, we prove that the multiplication operator Mzn is similar to n 1 Mz on A 2 α (D). (2000). 32A36, 46J40, 47A15. Mathematics Subject Classification

Similarity of analytic Toeplitz operators on the Bergman spaces

“…For another proof, see [7]. Even for a very special Toeplitz operator T z n on the weighted Bergman space A 2 α , the following result was established in [14] recently. We define the composition operator C B on A 2 α by…”

On quasi-similarity of multiplication operator on the weighted Bergman space in the unit ball

“…Throughout the rest of this paper, we will always assume that N ≥ 2 since it has been considered by Li [10] for the case N = 1. Moreover, we would like to point out that n stands for the multi-index (n…”

“…In 2007, Jiang and Li (see [8]) first obtained that analytic Toeplitz operator M B(z) is similar to ⊕ n 1 M z on the Bergman space if and only if B(z) is an n-Blaschke product. Next, Li (see [10]) in 2009 proved that multiplication operator M z n is similar to ⊕ n 1 M z on the weighted Bergman space. And then, Jiang and Zheng in [9] extended the main result in [8] to the weighted Bergman space.…”

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

“…on the Bergman space A 2 α (D) (see [11]). Now, we will investigate the situation on the Bergman space A 2 α (B n ) .…”