Geodesic
The resolvent of a Toeplitz operator may have arbitrary growth
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 175-177 
S. R. Treil'. The resolvent of a Toeplitz operator may have arbitrary growth. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 175-177. http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a18/
@article{ZNSL_1987_157_a18,
     author = {S. R. Treil'},
     title = {The resolvent of {a~Toeplitz} operator may have arbitrary growth},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {175--177},
     year = {1987},
     volume = {157},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a18/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Fix an arbitrary sequence $\{\lambda_n\}$ in the unit disc such that $\lim_n\lambda_n=1$ and any sequence $\{A_n\}$ of positive reals. Then there exists a continuous real $u$ on the unit circle such that the Toeplitz operator $T_\varphi$ (on the Hardy class $H^2$) with symbol $\varphi=e^{iu}$ satisfies $$ \|(T_\varphi-\lambda_nI)^{-1}\|>A_n $$