Abstract and Applied Analysis
Volume 2013 (2013), Article ID 342682, 10 pages
http://dx.doi.org/10.1155/2013/342682
Research Article

Fine Spectra of Upper Triangular Triple-Band Matrices over the Sequence Space ( )

Ali Karaisa1 and Feyzi Başar2

1Department of Mathematics, Necmettin Erbakan University, Karaciğan Mahallesi, Ankara Caddesi 74, 42060 Konya, Turkey
2Department of Mathematics, Fatih University, Hadımköy Campus, Büyükçekmece, 34500 Istanbul, Turkey

Received 27 September 2012; Revised 28 December 2012; Accepted 31 December 2012

Academic Editor: Simeon Reich

Copyright © 2013 Ali Karaisa and Feyzi Başar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 . The operator on sequence space on is defined by , where , with . In this paper we have obtained the results on the spectrum and point spectrum for the operator on the sequence space . Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the operator on the sequence space are also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator over the space and we give some applications.