Superoptimal singular values and indices of infinite matrix functions
V. V. Peller, Sergei Treil · Indiana University Mathematics Journal · 1995
We study the problem of finding a best approximation of a given bounded operator function Φ on the unit circle T by bounded operator functions Q analytic in the unit disk.We minimize not onlyWe show that if the Hankel operator H Φ is compact, then such an approximation (which is called superoptimal) exists and uniqe.We study related factorizations (thematic factorizations), establish invariance of their indices and prove an inequality between the singular values of the Hankel operator H Φ and the superoptimal singular values ess sup ζ∈T s j (Φ(ζ) -Q(ζ)).