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Monotone Thematic Factorizations of Matrix functions
by
Alberto A. Condori
Michigan State University
We study the so-called thematic factorizations of admissible very badly approximable matrix functions. These factorizations were introduced by V. V. Peller and N. J. Young (1994, J. Funct. Anal. 120, 300-343) for studying superoptimal approximation by bounded analytic matrix functions. As shown by Peller and Young, the thematic indices are not uniquely determined by the function itself. However, it was shown by R. B. Alexeev and V. V. Peller (2001, J. Funct. Anal. 179, 309-332) that the indices of a monotone (non-increasing) thematic factorization of an admissible very badly approximable matrix function are uniquely determined by the matrix function itself. We prove that it is always possible to find a monotone non-decreasing thematic factorization for an admissible very badly approximable matrix function. Our proof is constructive.
Date received: January 11, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavq-08.