Abstract
LetG be a matrix-valued function on the unit circle which is the sum of a continuous function and anH ∞ function. We establish an inequality between corresponding terms of the sequence of singular values of the Hankel operator {s j (H G )} and a sequence formed from the superoptimal singular values ofG with repetitions. The number of times each superoptimal singular value is repeated is a positive integer index which is the winding number of a related scalar function on the circle and gives information about the superoptimal error functionG-Q withQ∈H ∞. In the second part of the paper we establish a property of invariance of the sum of the indices corresponding to a particular superoptimal singular value. This establishes the truth of two conjectures made in [PeY].
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References
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The research was supported by an NSF grant in modern analysis.