Abstract Ces\`aro Spaces. I. Duality
Karol Le\'snik, Lech Maligranda

TL;DR
This paper explores the duality of abstract Cesàro spaces, generalizing known results for sequence and function spaces, and reveals significant differences in duality behavior between finite and infinite intervals.
Contribution
It provides a simple, elementary method to determine the duals of abstract Cesàro spaces, highlighting the general nature of the duality problem beyond specific cases.
Findings
Duals of abstract Cesàro spaces are characterized in a general setting.
Elementary proofs simplify understanding of Cesàro space duality.
Distinct duality phenomena occur between finite and infinite intervals.
Abstract
We study abstract Ces\`aro spaces , which may be regarded as generalizations of Ces\`aro sequence spaces and Ces\`aro function spaces on or , and also as the description of optimal domain from which Ces\`aro operator acts to . We find the dual of such spaces in a very general situation. What is however even more important, we do it in the simplest possible way. Our proofs are more elementary than the known ones for and . This is the point how our paper should be seen, i.e. not as generalization of known results, but rather like grasping and exhibiting the general nature of the problem, which is not so easy visible in the previous publications. Our results show also an interesting phenomenon that there is a big difference between duality in the cases of finite and infinite interval.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Advanced Harmonic Analysis Research
