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A Hahn-Banach theorem for complex semifields
Published online by Cambridge University Press: 17 April 2009
Abstract
The following form of the Hahn-Banach theorem is proved: Let X be a linear space over the complex semifield E and let f: S → E be a linear functional defined on a subspace S of X. If p: X → RΔ is a seminorm with the property that ∣f(s)∣ ≪ p(s) for all s in S, then f has a linear extension F to X with the property that ∣F(x)∣ ≪ p(x) for all x in X.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 2 , Issue 1 , February 1970 , pp. 129 - 133
- Copyright
- Copyright © Australian Mathematical Society 1970