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In this work, we determine the fine spectrum of the matrix operator ${\left( {\Delta _{uvw}^2} \right)^t}$ which is defined generalized upper triangular triple band matrix on ${l_1}$ . Also, we give the approximate point spectrum, defect spectrum and compression spectrum of the matrix operator ${\left( {\Delta _{uvw}^2} \right)^t}$ on ${l_1}

On the fine spectrum of generalized upper triangular triple-band matrices (Δ2uvw)t over the sequence space l1