A study on some paranormed sequence spaces due to Lambda–Pascal matrix

Yaying T., Başar F.

Acta Scientiarum Mathematicarum, vol.91, no.1, pp.161-180, 2025 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 91 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1007/s44146-024-00124-y
  • Journal Name: Acta Scientiarum Mathematicarum
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.161-180
  • Keywords: Alpha-, Beta- and Gamma-duals, Lambda–Pascal matrix, Matrix transformations, Schauder basis, Sequence space
  • Inonu University Affiliated: Yes

Abstract

This paper delves into the examination of algebraic and topological attributes associated with the domains c0(G,q), c(G, q), and ℓ∞(G,q) pertaining to the Lambda–Pascal matrix G in Maddox’s spaces c0(q), c(q), and ℓ∞(q), respectively. The determination of the Schauder basis and the computation of α-, β-, and γ-duals for these Lambda–Pascal paranormed spaces are carried out. The ultimate section is dedicated to elucidating the classification of the matrix classes (ℓ∞(G,q),ℓ∞), (ℓ∞(G,q),f), and (ℓ∞(G,q),c), concurrently presenting the characterization of specific other sets of matrix transformations in the space ℓ∞(G,q) as corollaries derived from the primary outcomes.