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Proyecciones (Antofagasta)

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DURNA, Nuh. Partition of the spectra for the lower triangular double band matrix as generalized difference operator Δ v over the sequence spaces c and 𝓵 p (1 < p < ∞). Proyecciones (Antofagasta) [online]. 2020, vol.39, n.1, pp.51-71. ISSN 0716-0917.


Let the sequence (v k ) is assumed to be either constant or strictly decreasing sequence of positive real numbers satisfying lim k→∞ v k = L > 0 and sup k v k ≤ 2L. Then the generalized difference operator Δ v is Δ v x = Δ v (x n ) = (v n x n − v n−1 x n−1 ) ∞ n=0 with x −1 = v −1 = 0. The aim of this paper is to obtain the approximate point spectrum, the defect spectrum and the compression spectrum of the operator Δ v and modified of the operator Δ v on the sequence spaces c and 𝓁 p (1 < p < ∞).

Keywords : Generalized difference operator; Approximate point spectrum; Defect spectrum; Compression spectrum.

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