Geodesic
Toeplitz condition numbers as an $H^\infty$ interpolation problem
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 36, Tome 355 (2008), pp. 173-179

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The condition numbers $CN(T)=\Vert T\Vert\cdot\Vert T^{-1}\Vert$ of Toeplitz and analyticToeplitz $n\times n$ matrices $T$ are studied. It is shown that the supremum of $CN(T)$ over all such matrices with $\Vert T\Vert\leq1$ and a given minimum of eigenvalues $r=\min_{i=1,\dots,n}|\lambda_i|>0$ behaves as the corresponding supremum over all $n\times n$ matrices (i.e., as $\frac1{r^n}$; Kronecker), and this equivalence is uniform in $n$ and $r$. The proof is based on the use of the Sarason–Sz.-Nagy–Foiaş commutant lifting theorem. Bibl. – 2 titles. 
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     author = {R. Zarouf},
     title = {Toeplitz condition numbers as an $H^\infty$ interpolation problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {173--179},
     publisher = {mathdoc},
     volume = {355},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_355_a6/}
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R. Zarouf. Toeplitz condition numbers as an $H^\infty$ interpolation problem. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 36, Tome 355 (2008), pp. 173-179. http://geodesic.mathdoc.fr/item/ZNSL_2008_355_a6/