  The spectrum of triangular band matrices defined on the sequence spaces where
the entries of each band is a constant or convergent sequence is well studied.
In this article, the spectrum and fine spectrum of a new generalised difference
operator defined by a lower triangular triple band matrix on the sequence space
$l_p (1 \leq p < \infty)$ are obtained where the bands are considered as
periodic sequences. The approximate point spectrum, defect spectrum,
compression spectrum and the Goldberg classification of the spectrum are also
discussed. Suitable examples are given in order to supplement the results.
Several special cases of our findings are discussed which confirm that our
study is more general and extensive.
