Title

Additivity and superadditivity in Lp spaces

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.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1017/S0305004100065920

Publication Date

1-1-1986

Journal Title

Mathematical Proceedings of the Cambridge Philosophical Society

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