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Algebra i Analiz, 2005, Volume 17, Issue 3, Pages 160–183 (Mi aa674)  

Research Papers

Approximation by analytic operator functions. Factorizations and very badly approximable functions

V. V. Pellera, S. R. Treilb

a Department of Mathematics, Michigan State University
b Department of Mathematics, Brown University
References:
Abstract: This is a continuation of our earlier paper [РТЗ]. We consider here operatorvalued functions (or infinite matrix functions) on the unit circle $\mathbb T$ and study the problem of approximation by bounded analytic operator functions. We discuss thematic and canonical factorizations of operator functions and study badly approximable and very badly approximable operator functions.
We obtain algebraic and geometric characterizations of badly approximable and very badly approximable operator functions. Note that there is an important difference between the case of finite matrix functions and the case of operator functions. Our criteria for a function to be very badly approximable in the case of finite matrix functions also guarantee that the zero function is the only superoptimal approximant. However in the case of operator functions this is not true.
Received: 30.11.2004
English version:
St. Petersburg Mathematical Journal, 2006, Volume 17, Issue 3, Pages 493–510
DOI: https://doi.org/10.1090/S1061-0022-06-00917-4
Bibliographic databases:
Document Type: Article
Language: English
Citation: V. V. Peller, S. R. Treil, “Approximation by analytic operator functions. Factorizations and very badly approximable functions”, Algebra i Analiz, 17:3 (2005), 160–183; St. Petersburg Math. J., 17:3 (2006), 493–510
Citation in format AMSBIB
\Bibitem{PelTre05}
\by V.~V.~Peller, S.~R.~Treil
\paper Approximation by analytic operator functions. Factorizations and very badly approximable functions
\jour Algebra i Analiz
\yr 2005
\vol 17
\issue 3
\pages 160--183
\mathnet{http://mi.mathnet.ru/aa674}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2167849}
\zmath{https://zbmath.org/?q=an:1153.47011}
\transl
\jour St. Petersburg Math. J.
\yr 2006
\vol 17
\issue 3
\pages 493--510
\crossref{https://doi.org/10.1090/S1061-0022-06-00917-4}
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    Алгебра и анализ St. Petersburg Mathematical Journal
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