Abstract
The area of ideals is important in the study of Analysis, algebra, Geometry and
Computer science. The various types of ideals have been studied, for example
m ideals and h ideals. The m ideals defined on real Banach spaces are
referred to as u - ideals. The natural examples of u - ideals with respect to
their biduals, are order continuous Banach lattices. Using the approximation
property, we shall study properties of u - ideals and their characterization. We
define the set of compact operators K X( ) on X to be u - ideals given that
X is a separable reflexive Banach space with approximation property if and
only if there is a sequence (Tn ) of finite rank of operators with lim 2 1 n n →∞ I T − =
and lim
n n →∞Tx x = . We shall show that u -ideals containing no copies of
sequences 1 are strict u - ideals.