On some study of the fine spectra of generalized difference operator Δ_a,b on ℓ_p (1<p<∞)

2018/07/08 by Riddhick Birbonshi, Birbonshi, Riddhick, Arnab Patra +3
Mathematics · #47A10 #47B37 #Approximation Theory and Sequence Spaces #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #math.FA #msc:47A10 #msc:47B37

paper · pdf · doi:10.48550/arxiv.1807.02849

18 pages

arxiv created 2018/07/08 · openalex publication_date 2018/07/08 · arxiv updated 2018/07/10 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we determine the spectrum, the point spectrum, the continuous spectrum and the residual spectrum of the generalized difference operator Δ_a,b on the sequence space ℓ_p (1< p < ∞) where the real sequences a=\a_k\ and b=\b_k\ are not necessarily convergent. Hence our results generalize the work given by Akhmedov and El-Shabrawy [Math. Slovaca 65~(5) (2015) 1137--1152] for the sequence space ℓ_p (1< p <∞).

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