2020/09/02 by José Bonet, Bonet, José, Werner J. Ricker +1
Mathematics · #46A11 #46A13 #47B37 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 46A45 #Secondary: 46A04
paper · pdf · doi:10.48550/arxiv.2009.01132
openalex publication_date 2020/09/02 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
The Fréchet (resp. (LB)) sequence spaces ces(p+) := ∩r > p ces(r), 1 ≤ p < ∞ (resp. ces (p-) := ∪ 1 < r < p ces (r), 1 < p ≤ ∞), are known to be very different to the classical sequence spaces ℓ_ p+ (resp., ℓ_p-). Both of these classes of non-normable spaces ces (p+), ces (p-) are defined via the family of reflexive Banach sequence spaces ces (p), 1 < p < ∞ . The dual Banach spaces d (q), 1 < q < ∞ , of the discrete Cesàro spaces ces (p), 1 < p < ∞, were studied by G. Bennett, A. Jagers and others. Our aim is to investigate in detail the corresponding sequence spaces d (p+) and d (p-), which have not been considered before. Some of their properties have similarities with those of ces (p+), ces (p-) but, they also exhibit differences. For instance, ces (p+) is isomorphic to a power series Fréchet space of order 1, whereas d (p+) is isomorphic to such a space of infinite order. Every space ces (p+), ces (p-) admits an absolute basis but, none of the spaces d (p+), d (p-) have any absolute basis.