2021/03/11 by Javad Mashreghi, Mashreghi, Javad, Pierre-Olivier Parisé +3
Mathematics · #40C15 (Primary) 40G10 #40J05 (Secondary) #41A10 #46E20 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2103.06631
openalex publication_date 2021/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that there exists a de Branges-Rovnyak space H(b) on the unit disk containing a function f with the following property: even though f can be approximated by polynomials in H(b), neither the Taylor partial sums of f nor their Cesàro, Abel, Borel or logarithmic means converge to f in H(b). A key tool is a new abstract result showing that, if one regular summability method includes another for scalar sequences, then it automatically does so for certain Banach-space-valued sequences too.