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- W2951837863 abstract "We study in this paper very badly approximable matrix functions on the unit circle $T$, i.e., matrix functions $Phi$ such that the zero function is a superoptimal approximation of $Phi$. The purpose of this paper is to obtain a characterization of the continuous very badly approximable functions. Our characterization is more geometric than algebraic characterizations earlier obtained in cite{PY} and cite{AP}. It involves analyticity of certain families of subspaces defined in terms of Schmidt vectors of the matrices $Phi(z)$, $zinT$. This characterization can be extended to the wider class of {em admissible} functions, i.e., the class of matrix functions $Phi$ such that the essential norm $|H_Phi|_{rm e}$ of the Hankel operator $H_Phi$ is less than the smallest nonzero superoptimal singular value of $Phi$. In the final section we obtain a similar characterization of badly approximable matrix functions." @default.
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- W2951837863 date "2003-03-15" @default.
- W2951837863 modified "2023-09-24" @default.
- W2951837863 title "Very badly approximable matrix functions" @default.
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- W2951837863 doi "https://doi.org/10.48550/arxiv.math/0303186" @default.
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