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Converses for the Dodds–Fremlin and Kalton–Saab theorems

Published online by Cambridge University Press:  24 October 2008

A. W. Wickstead
A. W. Wickstead
Affiliation:
The Queen's Universityof Belfast, BT7 1NN
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Extract

The two theorems in the title give conditions on Banach lattices E and F under which a positive operator from E into F, dominated by another positive operator with some property, must also have that property. The Dodds-Fremlin theorem says that this is true for compactness provided both E′ and F have order continuous norms, whilst the Kalton–Saab theorem establishes such a result for Dunford–Pettis operators provided F has an order continuous norm. These results were originally provided, in their full generality, in [3] and [5], respectively, whilst very readable proofs may be found in chapter 5 of [2] or §3·7 of [6].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 1 , July 1996 , pp. 175 - 179
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

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