2015/12/09 by Guillermo P. Curbera, Curbera, Guillermo P., Werner J. Ricker +1
Mathematics · #46E30 #46G10 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46E30 #msc:46G10
paper · pdf · doi:10.48550/arxiv.1512.02760
21 pages
arxiv created 2015/12/09 · openalex publication_date 2015/12/09 · arxiv updated 2015/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Cesàro function spaces Cesp=[C,Lp], 1≤ p≤∞, have received renewed attention in recent years. Many properties of [C,Lp] are known. Less is known about [C,X] when the Cesàro operator takes its values in a rearrangement invariant (r.i.) space X other than Lp. In this paper we study the spaces [C,X] via the methods of vector measures and vector integration. These techniques allow us to identify the absolutely continuous part of [C,X] and the Fatou completion of [C,X]; to show that [C,X] is never reflexive and never r.i.; to identify when [C,X] is weakly sequentially complete, when it is isomorphic to an AL-space, and when it has the Dunford-Pettis property. The same techniques are used to analyze the operator C:[C,X]→ X; it is never compact but, it can be completely continuous.