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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 381069, 19 pages
http://dx.doi.org/10.1155/2012/381069
Research Article

Fine Spectra of Upper Triangular Double-Band Matrices over the Sequence Space ,

Department of Mathematics, Faculty of Sciences, Konya Necmettin Erbakan University, Karacian Mahallesi, Ankara Caddesi 74, 42060 Konya, Turkey

Received 8 May 2012; Accepted 9 July 2012

Academic Editor: Antonia Vecchio

Copyright © 2012 Ali Karaisa. 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 operator on sequence space on is defined , where , and and are two convergent sequences of nonzero real numbers satisfying certain conditions, where . The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg's classification of the operator defined by a double sequential band matrix over the sequence space . Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator over the space .