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On operators which commute with analytic Toeplitz operators modulo the finite rank operators
Authors:Kunyu Guo   Kai Wang
Affiliation:School of Mathematics, Fudan University, Shanghai, 200433, People's Republic of China ; School of Mathematics, Fudan University, Shanghai, 200433, People's Republic of China
Abstract:It is shown that an operator $ S$ on the Hardy space $ H^2({mathbb{D}}^n)$ (or $ H^2({mathbb{B}}_n)$) commutes with all analytic Toeplitz operators modulo the finite rank operators if and only if $ S=T_g+F$. Here $ F$ is a finite rank operator, and in the case $ n=1$, $ g$ is a sum of a rational function and a bounded analytic function, and in the case $ ngeq 2$, $ g$ is a bounded analytic function.

Keywords:Hardy space   Toeplitz operator   finite rank operator
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