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arXiv · 2302.06770

Kernel-Summability Methods and the Silverman-Toeplitz Theorem

Pierre-Olivier Parisé
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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 $X$ 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.

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Pierre-Olivier Parisé. 2023-02-14. Kernel-Summability Methods and the Silverman-Toeplitz Theorem. https://arxiv.org/abs/2302.06770

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