Abstract
This paper concerns the spectrum and the fine spectrum of the discrete generalized Cesàro operator
C
t
, where
0
≤
t
<
1
, on Banach sequence spaces close to
ℓ
1
and
ℓ
∞
. We derive some compactness results for the operator
C
t
to describe the spectrum. Our technique involves standard operator theory and summability theory.