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Zapiski Nauchnykh Seminarov LOMI, 1987, Volume 157, Pages 175–177
(Mi znsl5217)
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This article is cited in 1 scientific paper (total in 1 paper)
Short communications
The resolvent of a Toeplitz operator may have arbitrary growth
S. R. Treil'
Abstract:
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
$$
\|(T_\varphi-\lambda_nI)^{-1}\|>A_n
$$
Citation:
S. R. Treil', “The resolvent of a Toeplitz operator may have arbitrary growth”, Investigations on linear operators and function theory. Part XVI, Zap. Nauchn. Sem. LOMI, 157, "Nauka", Leningrad. Otdel., Leningrad, 1987, 175–177
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https://www.mathnet.ru/eng/znsl5217 https://www.mathnet.ru/eng/znsl/v157/p175
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Abstract page: | 119 | Full-text PDF : | 38 |
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