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Abstract. The generalized difference operator  has been defined by Fathi and Lashkaripour:  with ,  are convergent sequences of nonzero real numbers satisfying certain conditions. The purpose of this paper is to completely determine the approximate point spectrum, the defect spectrum and the comprossion spectrum of the operator  on the sequence space . Also, with this division, the fine spectrum of generalized lower triangular double band matrices  which is given by Fathi and Lashkaripour in 2012, has been proved more shortly and different method on space. Keywords: Generalized difference operator, approximate point spectrum, defect spectrum, comprossion spectrum . Ozet. Genellestirilmis fark operatoru  Fathi ve Lashkaripour tarafindan tanimlanmistir:  bazi kosullari saglayan sifirdan farkli reel sayilarin yakinsak dizileri olmak uzere  biciminde tanimlanir. Burada  dir. Bu makalenin amaci  dizi uzayi uzerinde  operatorunun yaklasik nokta sepktrumunu, eksik spektrumunu ve sikistirilmis spektrumunu tam olarak belirlemektir. Ayrica bu ayrisim yardimiyla 2012 de Fathi ve Lashkaripour tarafindan verilen  genellestirilmis altucgensel cift bant matrisinin ince spektrumu  uzayi uzerinde daha farkli ve kisa bir yolla hesaplanmistir. Anahtar Kelimeler: genellestirilmis fark operatoru, yaklasik nokta spektum, eksik spektrum, sikistirilmis spektrum.

On The Fine Spectrum of Generalized Lower Triangular Double Band Matrices Over The Sequence Space