On the Modulus of Weakly Compact Operators and Strongly Additive Vector Measures

Klaus D. Schmidt
1988 Proceedings of the American Mathematical Society  
Aliprantis and Burkinshaw proved that each weakly compact operator from an AL-space into a KB-space has a weakly compact modulus. In the present paper it is shown that this is also true for weakly compact operators from a Banach lattice having an order continuous dual norm into an order complete AM-space with unit. A corresponding result is obtained for strongly additive vector measures.
doi:10.2307/2047324 fatcat:i5hony5gv5gxnomzzl6lvxnssi