数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 477-486.doi: 10.1016/S0252-9602(16)30014-5

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NOTES ON THE SPECTRAL PROPERTIES OF THE WEIGHTED MEAN DIFFERENCE OPERATOR G(u, v;Δ) OVER THE SEQUENCE SPACE l1

Vatan KARAKAYA1, Ezgi ERDOGAN2   

  1. 1. Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, Istanbul, Turkey;
    2. Department of Mathematics, Marmara University, Kadiköy, Istanbul, Turkey
  • 收稿日期:2014-09-24 修回日期:2015-01-11 出版日期:2016-04-25 发布日期:2016-04-25
  • 作者简介:Vatan KARAKAYA,E-mail:vkkaya@yahoo.com;Ezgi ERDOĞAN,E-mail:ezgi.erdogan@marmara.edu.tr

NOTES ON THE SPECTRAL PROPERTIES OF THE WEIGHTED MEAN DIFFERENCE OPERATOR G(u, v;Δ) OVER THE SEQUENCE SPACE l1

Vatan KARAKAYA1, Ezgi ERDOGAN2   

  1. 1. Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, Istanbul, Turkey;
    2. Department of Mathematics, Marmara University, Kadiköy, Istanbul, Turkey
  • Received:2014-09-24 Revised:2015-01-11 Online:2016-04-25 Published:2016-04-25

摘要:

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=ukvi (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.

关键词: Spectrum of an operator, weighted mean difference operator, sequence space

Abstract:

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=ukvi (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.

Key words: Spectrum of an operator, weighted mean difference operator, sequence space

中图分类号: 

  • 47A10