Spectra of the generalized difference operator on the sequence spaces bv0 and h

The spectra of the generalized difference operator B(r, s) in various sequence spaces have been investigated by many authors. Nevertheless, to the best of our knowledge, no contribution has appeared so far to study the problem in the common sequence spaces h and bv0.

In this paper, we fill this gap by analysing the spectrum of the operator B(r, s) on bv0 and h. Also, we explore some ideas of how to study the problem for a general form of the operator, namely, the operator ∆ab.