On the fine spectrum of the generalized difference operator <i>B</i>(<i>r</i>, <i>s</i>) over the sequence spaces <i>c</i>₀ and <i>c</i>

Abstract

We determine the fine spectrum of the generalized difference operator B ( r , s ) defined by a band matrix over the sequence spaces c 0 and c , and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operator Δ , and includes as other special cases the right shift and the Zweier matrices.