Abstract and Applied Analysis

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

Medine Yeşilkayagil and Feyzi Başar

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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 c 0 and c. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator Λ on the sequence spaces c 0 and c. Finally, we present a Mercerian theorem. Since the matrix Λ is reduced to a regular matrix depending on the choice of the sequence ( λ k ) having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 687393, 13 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511816

Digital Object Identifier
doi:10.1155/2013/687393

Mathematical Reviews number (MathSciNet)
MR3039140

Zentralblatt MATH identifier
1315.47004

Citation

Yeşilkayagil, Medine; Başar, Feyzi. On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences. Abstr. Appl. Anal. 2013 (2013), Article ID 687393, 13 pages. doi:10.1155/2013/687393. https://projecteuclid.org/euclid.aaa/1393511816


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