On the fine spectrum of the upper triangle double band matrix $\Delta^+$ on the sequence space $c_0$

Abstract

In this study, we determine the fine spectrum of the matrix operator $\Delta^+$ defined by an upper triangle double band matrix acting on the sequence space $c_0$ with respect to the Goldberg's classification. As a new development, we give the approximate point spectrum, defect spectrum and compression spectrum of the matrix operator $\Delta^+$ on $c_{0}$.