Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 36, Tome 355 (2008), pp. 173-179
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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/
@article{ZNSL_2008_355_a6,
author = {R. Zarouf},
title = {Toeplitz condition numbers as an $H^\infty$ interpolation problem},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {173--179},
year = {2008},
volume = {355},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_355_a6/}
}
TY - JOUR
AU - R. Zarouf
TI - Toeplitz condition numbers as an $H^\infty$ interpolation problem
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2008
SP - 173
EP - 179
VL - 355
UR - http://geodesic.mathdoc.fr/item/ZNSL_2008_355_a6/
LA - en
ID - ZNSL_2008_355_a6
ER -
%0 Journal Article
%A R. Zarouf
%T Toeplitz condition numbers as an $H^\infty$ interpolation problem
%J Zapiski Nauchnykh Seminarov POMI
%D 2008
%P 173-179
%V 355
%U http://geodesic.mathdoc.fr/item/ZNSL_2008_355_a6/
%G en
%F ZNSL_2008_355_a6
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.
