International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 60, Pages 3187-3203
doi:10.1155/S0161171204406498
On the Banach algebra ℬ(lp(α))
Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université du Havre, BP 4006 IUT Le Havre, Havre 76610 Le, France
Received 23 June 2004
Copyright © 2004 Bruno de Malafosse. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.