On the fine spectrum of the $\Lambda$ operator defined by a lambda matrix over the sequence space $c_{0}$ and $c$

The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg's classification of the operator $\Lambda$ defined by a 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 $\Lambda$ on the sequence spaces $c_{0}$ and $c$.