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Intertwining relations and extended eigenvalues for analytic Toeplitz operators

Intertwining relations and extended eigenvalues for analytic Toeplitz operators

We study the intertwining relation $XT_\varphi=T_\psi X$ where $T_\varphi $ and $T_\psi$ are the Toeplitz operators induced on the Hardy space $H^2$ by analytic functions $\varphi$ and $\psi$, bounded on the open unit disc~$\mathbb{U}$, and $X$ is a nonzero bounded linear operator on $H^2$. Our work centers on the connection …