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

Schmidt, Klaus D.

doi:10.1090/S0002-9939-1988-0934857-7

On the modulus of weakly compact operators and strongly additive vector measures
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by Klaus D. Schmidt

Proc. Amer. Math. Soc. 102 (1988), 862-866

DOI: https://doi.org/10.1090/S0002-9939-1988-0934857-7

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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.

References

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