Matuya, Wanyonyi John.Makila, Patrick.Achiles, Simiyu.Aywa, Shem.Sammy, Musundi.2019-05-092019-05-0920122277-4920http://erepository.kibu.ac.ke/handle/123456789/917The 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.enAttribution-NonCommercial-ShareAlike 3.0 United Stateshttp://creativecommons.org/licenses/by-nc-sa/3.0/us/IdealsU - idealsStrict uIdealsHermitianArticle