Kernel-Summability Methods and the Silverman-Toeplitz Theorem
Functional Analysis
2023-07-18 v3 Complex Variables
Abstract
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 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 -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.
Cite
@article{arxiv.2302.06770,
title = {Kernel-Summability Methods and the Silverman-Toeplitz Theorem},
author = {Pierre-Olivier Parisé},
journal= {arXiv preprint arXiv:2302.06770},
year = {2023}
}