Some geometric properties of the duals of Cesàro sequence spaces
MATHEMATICA SLOVACA, cilt.76, sa.2, ss.451-460, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 76 Sayı: 2
- Basım Tarihi: 2026
- Doi Numarası: 10.1515/ms-2025-1004
- Dergi Adı: MATHEMATICA SLOVACA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.451-460
- Anahtar Kelimeler: duals of Cesàro sequence spaces, rotundity, Schur's property, smoothness
- İstanbul Kültür Üniversitesi Adresli: Hayır
Özet
The spaces d(s) are defined for 0 <= s <= infinity. We consider the fundamental geometric properties of the d(s) spaces, isomorphic duals of the Cesaro sequence spaces ces(r) with 1/s + 1/r =1. We prove that for 1 <= s < infinity, the Banach spaces d(s) are Radon-Riesz spaces that are not rotund or smooth. Moreover, we show that the Banach lattice d(1) has Schur's property, just as i1 does. Finally, a characterization of norm totally bounded subsets of d(1) is also given.