Notes on the spectral properties of the weighted mean difference operator G (u, v; Δ) over the sequence space
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- 作者：Vatan KARAKAYAa ; vkkaya@yahoo.com" class="auth_mail" title="E-mail the corresponding author ; Ezgi ERDOĞANb ; ezgi.erdogan@marmara.edu.tr" class="auth_mail" title="E-mail the corresponding author
- 关键词：Spectrum of an operator ; weighted mean difference operator ; sequence space
- 刊名：Acta Mathematica Scientia
- 出版年：2016
- 出版时间：March 2016
- 年：2016
- 卷：36
- 期：2
- 页码：477-486
- 全文大小：361 K
文摘
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 
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.
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.