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Additivity and superadditivity in Lp-spaces

Published online by Cambridge University Press:  24 October 2008

S. J. Bernau
S. J. Bernau
Affiliation:
Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, U.S.A.
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Abstract

A simple proof is given that if X is a normed vector lattice, 1 ≼ p ≼ ∞, and the norm in X is p-additive, then the norm is p-superadditive if p < ∞. If p = ∞, then X satisfies Kakutani's classical M-space condition. The proof uses duality but is otherwise elementary.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 1 , July 1986 , pp. 133 - 136
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

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