Weak Dunford-Pettis Property for a Closed Sublattice of Compact Operators

Abstract

For several Banach lattices

E and F, if K(E; F

E to F

M of K(E; F

'x : M ! F and y : M ! E

'x(T) = Tx and y (T) = T y

x

2 E, y 2 F and T 2 M

.

for

are

almost Dunford{Pettis operators, where

) to have the weak Dunford{Pettis

property is that all evaluation operators

, it is shown that a necessary and sucient

condition for a closed subspace

) denotes the space

of all compact operators from