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 $({\lambda }_k)$ having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.