Abstract
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 (( ) , . ).