Notes on the spectral properties of the weighted mean difference operator G (u, v; δ) over the sequence space ℓ1

KARAKAYA V., ERDOĞAN E.

Acta Mathematica Scientia, cilt.36, sa.2, ss.477-486, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/s0252-9602(16)30014-5
  • Dergi Adı: Acta Mathematica Scientia
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.477-486
  • Anahtar Kelimeler: Spectrum of an operator, weighted mean difference operator, sequence space, FINE SPECTRUM, FACTORABLE MATRICES, BV(P), L(P)
  • Marmara Üniversitesi Adresli: Evet

Özet

© 2016 Wuhan Institute of Physics and Mathematics.In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014(2014), Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G (u, v; δ) over the sequence space ℓ1. The product operator G (u, v; δ) over ℓ1 is defined by (G(u,v; δ)x)k=∑i=0kukvi(xi-xi-1) with xk = 0 for all k < 0, where x = (xk) ∈ ℓ1, and u and v are either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G (u, v; δ) on the sequence space ℓ1.