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Isotone measures on groups

Published online by Cambridge University Press:  24 October 2008

W. Moran  and
J. H. Williamson
W. Moran
Affiliation:
University of Adelaide and University of York
J. H. Williamson
Affiliation:
University of Adelaide and University of York
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Extract

If E and F are ordered spaces, a map T: E → F is positive if

The map T is bi-positive if f ≥ 0 ⇔ Tf ≥ 0. It is a natural problem to seek information about the positive and bi-positive linear maps between pairs of ordered vector spaces. The present study is an attempt to elucidate one facet of this general problem (see, for example, (2), vol. II, § 16·7·1, p. 278).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 89 - 107
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Bourbaki, N.Topologie generate, chs. 3, 4 (3rd ed.). Actualités Sci. et Ind. 1143 (Paris, Hermann, 1960).Google Scholar
(2)Edwards, R. E.Fourier series (New York, Holt, Rinehart and Winston, 1967).Google Scholar
(3)Greenleaf, F. P.Invariant means on topological groups. Van Nostrand Mathematical Studies No. 16 (New York, Van Nostrand-Reinhold, 1969).Google Scholar
(4)Hewitt, E. and Ross, K. A.Abstract harmonic analysis, vol. I (Berlin, Springer-Verlag, 1963).Google Scholar
(5)Moran, W.Isotone measures on locally compact groups. J. London Math. Soc. (2nd series) 5 (1972), 347–355.CrossRefGoogle Scholar
(6)Peeks, B. J.LP(G)-isotone measures. Math. Proc. Cambridge Philos. Soc. 78 (1975), 471–481.Google Scholar
(7)Pym, J. S.A note on the Kawada-into theorem. Proc. Edinburgh Math. Soc. 13 (1963), 295–296.CrossRefGoogle Scholar
(8)Williamson, J. H.On theorems of Kawada and Wendel. Proc. Edinburgh Math. Soc. 11 1958, 71–77.CrossRefGoogle Scholar
(9)Williamson, J. H. Isotone measures, 1948–1973. Functional analysis and its applications (International Conference, Madras, 1973), pp. 573–583 (Lecture Notes in Mathematics, no. 399; Berlin, Springer-Verlag, 1974).Google Scholar