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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 60, Pages 3187-3203
http://dx.doi.org/10.1155/S0161171204406498

On the Banach algebra (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 Hindawi Publishing Corporation. 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 (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.