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Additive Functionals on Groups*

Published online by Cambridge University Press:  24 October 2008

Allan Hayes
Allan Hayes
Affiliation:
Massachusetts Institute of Technology
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Extract

The kernel of a non-trivial linear functional φ on a linear space E is a maximal proper linear subspace of E which determines φ up to a non-zero multiple. Does a similar result hold for homomorphisms of a group G into the additive group R of the real numbers?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 196 - 205
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Birkhoff, G.Lattice theory (American Math. Soc. Colloquium Publ. vol. xxv; New York, 1948).Google Scholar
(2)Bonsall, F. FSublinear functionals and ideals in partially-ordered vector spaces. Proc. London Math. Soc. (3), 4 (1954), 402–417.CrossRefGoogle Scholar
(3)Bonsall, F. FRegular ideals of partially-ordered spaces. Proc. London Math. Soc. (3), 6 (1956), 626–640.CrossRefGoogle Scholar
(4)Bourbaki, N.Intégration, Ch. 1 (Actualités Sci. Ind. no. 1175; Hermann; Paris, 1952).Google Scholar
(5)Day, M. MNormed linear spaces (Ergeb. d. Math. N. F. Heft 21; Springer; Berlin-Göttingen-Heidelberg, 1958).CrossRefGoogle Scholar
(6)Fan, KY.Partially-ordered additive groups of continuous functions. Ann. of Math. (2), 51 (1950), 409–427.CrossRefGoogle Scholar
(7)Fleischer, I.Functional representation of partially-ordered groups. Ann. of Math. (2), 64 (1956), 260–263.CrossRefGoogle Scholar
(8)Halperin, I.The supremum of a family of additive functions. Canadian J. Math. 4 (1952), 463–479.CrossRefGoogle Scholar
(9)Hammer, P. CMaximal convex sets. Duke Math. J. 22 (1955), 103–106.CrossRefGoogle Scholar
(10)Hoffman, K. and Singer, I. MMaximal subalgebras of C(Γ). American J. Math. 79 (1957), 295–305.CrossRefGoogle Scholar
(11)Kakutani, S.Concrete representation of abstract (M)-spaces. Ann. of Math. (2), 42 (1941), 994–1024.CrossRefGoogle Scholar
(12)Kuller, R. GLocally convex topological vector lattices and their representations. Michigan Math. J. 5 (1958), 83–90.CrossRefGoogle Scholar
(13)Namioka, I.Partially-ordered linear topological spaces (Mem. American Math. Soc. no. 24; Providence, R.I., 1957).CrossRefGoogle Scholar
(14)Stone, M. HA general theory of spectra. II. Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 83–87.CrossRefGoogle Scholar