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

doi:10.1016/S0252-9602(16)30014-5

Abstract

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=u_kv_i (x_i-x_i-1) with x_k=0 for all k<0, where x=(x_k)∈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

CLC Number:

47A10

Vatan KARAKAYA, Ezgi ERDOGAN. NOTES ON THE SPECTRAL PROPERTIES OF THE WEIGHTED MEAN DIFFERENCE OPERATOR G(u, v;Δ) OVER THE SEQUENCE SPACE l₁[J].Acta mathematica scientia,Series B, 2016, 36(2): 477-486.

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

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