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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.1 Antofagasta feb. 2020

http://dx.doi.org/10.22199/issn.0717-6279-2020-01-0004 

Artículos

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 < ∞)

1Sivas Cumhuriyet University, Dept. of Mathematics, Sivas, Turkey. E-mail: ndurna@cumhuriyet.edu.tr

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 < ∞).

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

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Full text available only in PDF format.

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Received: November 2018; Accepted: June 2019

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