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

Source 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.