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Lattice bounding, Radonifying and summing mappings

Published online by Cambridge University Press:  24 October 2008

D. J. H. Garling
D. J. H. Garling
Affiliation:
St John's College, Cambridge
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Extract

There are several known results concerning Radonifying and summing properties of linear mappings in terms of their transposed operators. Thus Schwartz has shown that a sufficient condition for a mapping to be p-Radonifying is that its transposed mapping should be p-decomposing, and that this condition is also necessary if the image space has good topological properties. But as Schwartz observes, these properties are seldom observed by biduals of Banach spaces with their weak-topologies, which arise when 0 ≤ p ≤ 1. This suggests that it would be worth looking for a weaker condition than ‘p-decomposing’.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 2 , March 1975 , pp. 327 - 333
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

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