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Proceedings of the American Mathematical Society

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On the modulus of weakly compact operators and strongly additive vector measures


Author: Klaus D. Schmidt
Journal: Proc. Amer. Math. Soc. 102 (1988), 862-866
MSC: Primary 47B55; Secondary 28B15, 46G10, 47B38
DOI: https://doi.org/10.1090/S0002-9939-1988-0934857-7
MathSciNet review: 934857
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Abstract: 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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934857-7
Keywords: Banach lattices, weakly compact operators, strongly additive vector measures
Article copyright: © Copyright 1988 American Mathematical Society