We give some properties of the Banach algebra of bounded operators
ℬ(lp(α))
for 1≤p≤∞,
where lp(α)=(1/α)−1∗lp. Then we deal with the continued fractions and give some properties of the operator Δh
for h>0
or integer greater than or equal to one mapping lp(α)
into itself for p≥1
real. These results extend, among other things, those
concerning the Banach algebra Sα
and some results on the continued fractions.