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On the Biadjoint of Riesz-like homomorphisms on partially ordered vector spaces

Published online by Cambridge University Press:  17 April 2009

Gerard Buskes  and
Jamie Summerville
Gerard Buskes
Affiliation:
Department of MathematicsThe University of MississippiUniversity MS 38677-9701United States of America
Jamie Summerville
Affiliation:
Department of MathematicsThe University of MississippiUniversity MS 38677-9701United States of America
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Abstract

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We generalise to partially ordered vector spaces, with a new technique, Arendt's approach to Kim's characterisation of Riesz homomorphisms.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 473 - 481
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Aliprantis, C.D. and Burkinshaw, O., Positive operators (Academic Press, Orlando, 1985).Google Scholar
[2]Arendt, W., Über das Spektrum regularen Operatoren, (Ph.D. Dissertation) (University of Tübingen, 1979).Google Scholar
[3]Buskes, G. and van Rooij, A., ‘The vector lattice cover of certain partially ordered groups’, J. Austral. Math. Soc. 54 (1993), 352–367.CrossRefGoogle Scholar
[4]Buskes, G. and van Rooij, A., ‘Hahn-Banach for Riesz homomorphisms’, Indag. Math. 92 (1989), 25–34.CrossRefGoogle Scholar
[5]Conrad, P.F., ‘Minimal vector lattice covers’, Bull. Austral. Math. Soc. 4 (1971), 35–39.CrossRefGoogle Scholar
[6]Jellett, F., ‘Homomorphisms and inverse limits of Choquet simplexes’, Math. Z. 103 (1968), 219–226.CrossRefGoogle Scholar
[7]Fuchs, L., Riesz vector spaces and Riesz algebras, Queen's Papers in Pure and Applied Mathematics 1 (Queens University, Kingston, On, 1966).Google Scholar
[8]Kim, J., ‘The characterization of a lattice homomorphism’, Canad J. Math. 27 (1975), 172–175.CrossRefGoogle Scholar
[9]Lacey, H.E., The isometric theory of classical Banach spaces (Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar
[10]Meyer-Nieberg, P., Banach lattices (Springer-Verlag, Berlin, Heidelberg, New York, 1991).CrossRefGoogle Scholar
[11]Peressini, A.L., Ordered topological vector spaces (Harper and Row, New York, 1967).Google Scholar
[12]Takeo, F., ‘On a simplex homomorphism’, in Natural Science Report 34 (Ochanomizu University, 1983), pp. 53–59.Google Scholar
[13]Takeo, F., ‘On a simplex homomorphism II’, in Natural Science Report 35 (Ochanomizu University, 1984), pp. 47–56.Google Scholar
[14]Wickstead, A.W., ‘The spectrum of an R-homomorphism’, J. Austral. Math. Soc. 23 (1977), 42–45.CrossRefGoogle Scholar
[15]Zaanen, A.C., Riesz spaces II (North-Holland, Amsterdam, 1983).Google Scholar