Duals of Cesaro sequence vector lattices, Cesaro sums of Banach lattices, and their finite elements

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GÖNÜLLÜ U., Polat F., Weber M. R.

ARCHIV DER MATHEMATIK, cilt.120, sa.6, ss.619-630, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 120 Sayı: 6
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s00013-023-01840-7
  • Dergi Adı: ARCHIV DER MATHEMATIK
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.619-630
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

In this paper, we study the ideals of finite elements in special vector lattices of real sequences, first in the duals of Cesaro sequence spaces ces(p) for p is an element of{0}boolean OR[1,infinity) and, second, after the Cesaro sum ces(p)(X) of a sequence of Banach spaces is introduced, where p = infinity is also allowed, we characterize their duals and the finite elements in these sums if the summed up spaces are Banach lattices. This is done by means of a remarkable extension of the corresponding result for direct sums.