Fine Spectra of Upper Triangular Triple-Band Matrices over the Sequence Space ℓp (0<p<∞). (20th March 2013)

• Record Type: Journal Article
• Authors: Karaisa, Ali; Başar, Feyzi
• Other Names: Reich Simeon Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-03-20
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/342682
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : The fine spectra of lower triangular triple-band matrices have been examined by several authors (e.g., Akhmedov (2006), Başar (2007), and Furken et al. (2010)). Here we determine the fine spectra of upper triangular triple-band matrices over the sequence space ℓ p . The operator A ( r, s, t ) on sequence space on ℓ p is defined by A ( r, s, t ) x = ( r x k + s x k + 1 + t x k + 2 ) k = 0 ∞, where x = ( x k ) ∈ ℓ p, with 0 < p < ∞ . In this paper we have obtained the results on the spectrum and point spectrum for the operator A ( r, s, t ) on the sequence space ℓ p . Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the operator A ( r, s, t ) on the sequence space ℓ p are also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator A ( r, s, t ) over the space ℓ p and we give some applications.