Banach Journal of Mathematical Analysis

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

Li Zhang and Ze-Hua Zhou

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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

Subjects
Primary: 47B38: Operators on function spaces (general)
Secondary: 45P05: Integral operators [See also 47B38, 47G10] 47G10: Integral operators [See also 45P05] 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 47B33: Composition operators 33B30: Higher logarithm functions 46E15: Banach spaces of continuous, differentiable or analytic functions

Keywords
Hilbert-Schmidt operator composition operator weighted Bergman space unit ball

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


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