Abstract
In this paper we have shown that if $\phi\in (L_h^2)^{\perp}\cap L^{\infty}$, $\phi\neq 0$, then $\text{ker\,}T_{\phi}=\text{ker\,}T^*_{\phi}=\text{sp\,}\{1\}$ and therefore finite-dimensional subspaces of $L_a^2$. Further, if $\phi\in L^{\infty}(\D)$, $\phi\neq 0$, then it is shown that the Toeplitz operator $T_{\phi}$ cannot be of finite rank.
Citation
Namita Das. "Invariant subspaces and kernels of Toeplitz operators on the Bergman space." Rocky Mountain J. Math. 44 (1) 35 - 56, 2014. https://doi.org/10.1216/RMJ-2014-44-1-35
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