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, 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.