International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 50, Pages 2695-2704
On the sublinear operators factoring through
Department of Mathematics, M'sila University, P.O. Box 166, Ichbilia, M'sila 28105, Algeria
Received 15 March 2003
Copyright © 2004 Lahcène Mezrag and Abdelmoumene Tiaiba. 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.
Let . Let be a bounded sublinear
operator from a Banach space into an
be the set of all linear operators .
In the present paper, we will show the following. Let be a positive
constant. For all in , (i.e.,
admits a factorization of the form
is a bounded linear operator with , is the bounded
operator of multiplication by which is in (),
and is the constant
of -convexity of ) if and only if admits the same
factorization; This is under the supposition that is latticially bounded. Without this condition
this equivalence is not true in general.