Browsing by Author "Shem, Aywa"

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    Equivalent Banach operator ideal norms’’
    (2012-01) Musundi, S. Wambomba; Shem, Aywa; Fourie, Jan
    Let X, Y be Banach spaces and consider the w'-topology (the dual weak operator topology) on the space (L(X, Y) of bounded linear operators from X into X with the uniform operator norm. L w' (X, Y) is the space of all T ∈ L(X, Y) for which there exists a sequence of compact linear operators (Tn) ⊂ K(X, Y) such that T = w' - lim nT n. Two equivalent norms, on L w'(X, Y) are considered. We show that and Banach operator ideals.
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    On Characterization of u-ideals determined by sequences’’
    (2013) Matuya, wanyonyi john; Makila, Patrick; Simiyu, Achiles; Shem, Aywa; Musundi, Sammy
    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