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Abstract and Applied Analysis
Volume 2013, Article ID 687393, 13 pages
http://dx.doi.org/10.1155/2013/687393
Research Article

On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences

1Department of Mathematics, Uşak University, 1 Eylül Campus, 64200 Uşak, Turkey
2Department of Mathematics, Fatih University, The Hadimköy Campus, Büyükçekmece, 34500 İstanbul, Turkey

Received 28 September 2012; Accepted 18 January 2013

Academic Editor: Pavel Kurasov

Copyright © 2013 Medine Yeşilkayagil 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 main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the operator defined by the lambda matrix over the sequence spaces and c. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator on the sequence spaces and c. Finally, we present a Mercerian theorem. Since the matrix is reduced to a regular matrix depending on the choice of the sequence having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.