The Hahn sequence space generated by the Cesàro mean of order m

Savaşcı M., Başar F.

ACTA SCIENTIARUM MATHEMATICARUM, vol.90, pp.53-72, 2024 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 90
  • Publication Date: 2024
  • Doi Number: 10.1007/s44146-023-00098-3
  • Journal Name: ACTA SCIENTIARUM MATHEMATICARUM
  • Journal Indexes: Scopus
  • Page Numbers: pp.53-72
  • Keywords: Matrix domain, Matrix mappings, Sequence space, α -, β - and γ -duals
  • Uşak University Affiliated: Yes

Abstract

Hahn (Math Phys 32:3–88, 1922) defined the sequence space h. The main purpose of this study is to introduce the new Hahn sequence space h(Cm) as the domain of Cesàro mean of order m and give some topological properties of the space h(Cm) . Moreover, we determine the alpha-, beta- and gamma-duals of the space h(Cm) and characterize the classes (ℓ1: h) , (h: ℓp) , (h(Cm) : V1) and (V2: h(Cm)) of matrix transformations, where 1 < p< ∞ , V1∈ { ℓ∞, c, c, ℓp} and V2 is any given sequence space. Finally, we compute the norm of the operators belonging to B(ℓ1, h(Cm)) and determine the Hausdorff measure of noncompactness of the operators in B(ℓ1, h(Cm)) .