Browsing by Author "Sammy, Musundi."

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    On characterization of u-ideals determined by sequences
    (2012) Matuya, Wanyonyi John.; Makila, Patrick.; Achiles, Simiyu.; Aywa, Shem.; Sammy, Musundi.
    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.
  • Thumbnail Image
    Item
    Unconditional ideals in Banach spaces
    (Scientific advances, 2012-07-14) Sammy, Musundi.; Aywa, Shem.; Fourie, Jan.; Matuya, John Wanyonyi .
    Let wL ′ denote the assignment which associates with each pair of Banach spaces X , Y, the vector space L ( ) X Y w , ′ and K(X, Y ) be the space of all compact linear operators from X to Y. Let T L ( ) X Y w , ′ ∈ and suppose () ( ) Tn ⊂ K X, Y converges in the dual weak operator topology (w′) of T. Denote by Ku(( )) Tn the finite number given by (( )) { { max , 2 }}. sup : n n n Ku Tn = T T − T ∈N The u-norm on L ( ) X Y w , ′ is then given by { ( ( ) ) ( )} , , . T : inf K T : T w lim Tn Tn K X Y u u n n = = ′ − ∈ It has been shown that (( ) ) u wL X, Y . ′ is a Banach operator ideal. We find conditions for K( ) X, Y to be an unconditional ideal in (( ) , . ).