A Dodds–Fremlin Property for Asplund and Radon–Nikodým Operators |
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Authors: | Coenraad CA Labuschagne |
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Institution: | (1) School of Mathematics, University of the Witwatersrand, Johannesburg, Private Bag X3, 2050, WITS, South Africa |
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Abstract: | Let E and F be Banach lattices and let S, T: E→ F be positive operators such that 0≤ S≤ T. It is shown that if T is a Radon–Nikodym operator, F has order continuous norm and E and F both have (Schaefer's) property (P), then S is a Radon–Nikodym operator; also, if T is an Asplund operator, E' has order continuous norm and E has property (P), then S is an Asplund operator. |
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Keywords: | Primary 47B65 Secondary 46B22 |
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