Ces\'aro sums and algebra homomorphisms of bounded operators
Luciano Abadias, Carlos Lizama, Pedro J. Miana, M. Pilar Velasco

TL;DR
This paper explores the relationship between algebra homomorphisms on subalgebras of ^1() and Ces sums of bounded operators on Banach spaces, providing new characterizations and bounds.
Contribution
It establishes a characterization of -bounded operators via algebra homomorphisms and introduces methods involving sequence kernels and fractional calculus.
Findings
Improved bounds for Abel means
New insights into -boundedness of resolvent operators
Examples of bounded homomorphisms
Abstract
Let be a complex Banach space. The connection between algebra homomorphisms defined on subalgebras of the Banach algebra and the algebraic structure of Ces\`{a}ro sums of a linear operator is established. In particular, we show that every -bounded operator induces - and is in fact characterized - by such an algebra homomorphism. Our method is based on some sequence kernels, Weyl fractional difference calculus and convolution Banach algebras that are introduced and deeply examined. To illustrate our results, improvements to bounds for Abel means, new insights on the boundedness of the resolvent operator for temperated -times integrated semigroups, and examples of bounded homomorphisms are given in the last section.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Differential Equations and Boundary Problems · Advanced Harmonic Analysis Research
