2014/01/24 by Karol Leśnik, Leśnik, Karol, Lech Maligranda +1
Mathematics · #46B20 #46B42 #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B20 #msc:46B42 #msc:46E30
paper · pdf · doi:10.48550/arxiv.1401.6415
20 pages
openalex publication_date 2014/01/24 · arxiv created 2014/03/20 · arxiv updated 2014/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study abstract Cesàro spaces CX, which may be regarded as generalizations of Cesàro sequence spaces cesp and Cesàro function spaces Cesp(I) on I = [0,1] or I = [0,∞), and also as the description of optimal domain from which Cesàro operator acts to X. 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 cesp and Cesp(I). 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.