1995/11/28 by Vladimir Peller, Vladimir V. Peller, N. J. Young +3
Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Approximation and Integration #math.FA
paper · pdf · doi:10.48550/arxiv.math/9511214
arxiv created 1995/11/28 · openalex publication_date 1995/11/28 · arxiv updated 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \A be the operator which assigns to each m × n matrix-valued function on the unit circle with entries in H^∞ + C its unique superoptimal approximant in the space of bounded analytic m × n matrix-valued functions in the open unit disc. We study the continuity of \A with respect to various norms. Our main result is that, for a class of norms satifying certain natural axioms, \A is continuous at any function whose superoptimal singular values are non-zero and is such that certain associated integer indices are equal to 1. We also obtain necessary conditions for continuity of \A at point and a sufficient condition for the continuity of superoptimal singular values.