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 < ∞)
Abstract 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...
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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2020
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000100051 |
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| Sumario: | Abstract 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 < ∞). |
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