## Abstract and Applied Analysis

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

#### 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 $\mathrm{\Lambda }$ on the sequence spaces ${c}_{0}$ and c. Finally, we present a Mercerian theorem. Since the matrix $\mathrm{\Lambda }$ is reduced to a regular matrix depending on the choice of the sequence $\left({\lambda }_{k}\right)$ 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

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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