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

Creative Commons License

GÖNÜLLÜ U., Polat F., Weber M. R.

ARCHIV DER MATHEMATIK, vol.120, no.6, pp.619-630, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 120 Issue: 6
  • Publication Date: 2023
  • Doi Number: 10.1007/s00013-023-01840-7
  • Journal Name: ARCHIV DER MATHEMATIK
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.619-630
  • Istanbul Kültür University Affiliated: Yes

Abstract

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.