Badly approximable matrix functions and canonical factorizations (Q2733851)

The authors study the problem of approximation of matrix functions on the unit circle by bounded analytic matrix functions in the unit disk. They introduce canonical and partial canonical factorizations and characteristic classes of badly approximable and very badly approximable matrix functions in terms of such factorizations. Unlike thematic factorizations introduced in \textit{V. V. Peller} and \textit{N. J. Young} [J. Funct. Anal. 120, No. 2, 300-343 (1994; Zbl 0808.47011)]. Canonical factorizations have an important invariance property. Their factors are uniquely determined modulo constant unitary factors.