Invariance properties of thematic factorizations of matrix functions

Details Invariance properties of thematic factorizations of matrix functions Invariance properties of thematic factorizations of matrix functions

2001-01-22

arxiv.org/abs/math/0101182v2

Mathematics

Functional Analysis

20 pages

Scientific paper

We study the problem of invariance of indices of thematic factorizations. Such factorizations were introduced in [PY1] for studying superoptimal approximation by bounded analytic matrix functions. As shown in [PY1], the indices may depend on the choice of a thematic factorization. We introduce the notion of a monotone thematic factorization. The main result shows that under natural assumptions a matrix function that admits a thematic factorization also admits a monotone thematic factorization and the indices of a monotone thematic factorization are uniquely determined by the matrix function itself. We obtain similar results for so-called partial thematic factorizations.

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