NOTES ON THE SPECTRAL PROPERTIES OF THE WEIGHTED MEAN DIFFERENCE OPERATOR G(u,v;?) OVER THE SEQUENCE SPACE ?_1  

作　　者：Vatan KARAKAYA Ezgi ERDOGAN 

机构地区：[1]Department of Mathematical Engineering,Yzldiz Technical University,Davutpasa,Istanbul,Turkey [2]Department of Mathematics,Marmara University,Kadikoy,Istanbul,Turkey

出　　处：《Acta Mathematica Scientia》2016年第2期477-486,共10页数学物理学报（B辑英文版）

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; A） over the sequence space e1. The product operator G （u, v; △） over l1 is defined by （G（u,v;△）x）k=^k∑i=0ukvi（xi- xi-1） with xk = 0 for all k 〈 0, where x = （xk）∈e1,and u and v axe 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; △） on the sequence space gl.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; A） over the sequence space e1. The product operator G （u, v; △） over l1 is defined by （G（u,v;△）x）k=^k∑i=0ukvi（xi- xi-1） with xk = 0 for all k 〈 0, where x = （xk）∈e1,and u and v axe 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; △） on the sequence space gl.

关 键 词：Spectrum of an operator weighted mean difference operator sequence space 

分 类 号：O177[理学—数学]