## Banach Journal of Mathematical Analysis

### Hilbert-Schmidt differences of composition operators between the weighted Bergman spaces on the unit ball

#### Abstract

Let $\varphi,\psi$ be the analytic self-maps of the unit ball ${\mathbb B}$, we characterize the Hilbert-Schmidt differences of two composition operator $C_\varphi$ and $C_\psi$ on weighted Bergman space $A_\alpha^2$, and give some conclusions about the topological structure of $\mathcal{C}(A_\alpha^2)$, the space of all bounded composition operators on $A_\alpha^2$ endowed with operator norm.

#### Article information

Source
Banach J. Math. Anal., Volume 7, Number 1 (2013), 160-172.

Dates
First available in Project Euclid: 22 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1358864556

Digital Object Identifier
doi:10.15352/bjma/1358864556

Mathematical Reviews number (MathSciNet)
MR3004274

Zentralblatt MATH identifier
1281.47014

#### Citation

Zhang, Li; Zhou, Ze-Hua. Hilbert-Schmidt differences of composition operators between the weighted Bergman spaces on the unit ball. Banach J. Math. Anal. 7 (2013), no. 1, 160--172. doi:10.15352/bjma/1358864556. https://projecteuclid.org/euclid.bjma/1358864556