Abstract

We give some properties of the Banach algebra of bounded operators (lp(α)) for 1p, where lp(α)=(1/α)1lp. 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 p1 real. These results extend, among other things, those concerning the Banach algebra Sα and some results on the continued fractions.