2023/02/14 by Pierre-Olivier Parisé, Parisé, Pierre-Olivier
Mathematics · #40D05 #40J05 #46E20 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #primary 40C10 #secondary 41A10
paper · pdf · doi:10.48550/arxiv.2302.06770
openalex publication_date 2023/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce kernel-summability methods in Banach spaces using the vector-valued integrals and prove an analogue of the Silverman-Toeplitz Theorem for regular kernel-summability methods. We also show that if X is a Banach space and one kernel-summability method is included in another kernel-summability method for scalar-valued functions, then the first method is included in the second method, for X-valued functions. This extends a previous result from Javad Mashreghi, Thomas Ransford and the author. We then apply these abstract results to the summability of Taylor series of functions in a Banach space of holomorphic functions on the unit disk.