Matuya, wanyonyi johnMakila, PatrickSimiyu, AchilesShem, AywaMusundi, Sammy2020-10-052020-10-052013Asian Journal of Current Engineering and Maths1: 5 Sep –Oct(2012) 247 – 250.22774920https://www.researchgate.net/profile/http://repository.chuka.ac.ke/handle/chuka/1381The 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 - idealsenIdeals,u - idealsstrict u - idealshermitianArticle