Spectrum and fine spectrum of the upper triangular matrix U(r, s) over the sequence spaces

Abstract

Fine spectra of various matrix operators on different sequence spaces have been investigated by several authors. Recently, some authors have determined the approximate point spectrum, the defect spectrum and the compression spectrum of various matrix operators on different sequence spaces. Here in this article we have determined the spectrum and fine spectrum of the upper triangular matrix U(r,s) on the sequence space cs. In a further development, we have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator U(r,s) on the sequence space cs.