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A Hahn-Banach theorem for complex semifields

Published online by Cambridge University Press:  17 April 2009

Howard Anton  and
W.J. Pervin
Howard Anton
Affiliation:
Drexel Institute of Technology, Philadelphia, Pennsylvania.
W.J. Pervin
Affiliation:
Drexel Institute of Technology, Philadelphia, Pennsylvania.
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Abstract

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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

References

[1]Antonovskiĭ, M.Ja., Boltjanskiĭ, V.G. and Sarymsakov, T.A., Topologioal Semifields (Russian), (Izdat. Sam. GU, Tashkent, 1960).Google Scholar
[2]Iséki, Kiyoshi and Kasahara, Shouro, “On Hahn-Banach type extension theorem”, Proc. Japan Acad. 41 (1965), 29–30.Google Scholar
[3]Kleiber, Martin and Pervin, W.J., “A Hahn-Banach theorem for semifields”, J. Austral. Math. Soc. 10 (1969), 20–22.CrossRefGoogle Scholar