International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 57-60, Pages 3187-3203
doi:10.1155/S0161171204406498

On the Banach algebra ℬ(lp(α))

Abstract

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.