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Positivity

, Volume 9, Issue 3, pp 293–325 | Cite as

Representations of Positive Projections I

  • W. A. J. Luxemburg
  • B. De Pagter
Article

Abstract

In this paper we start the development of a general theory of Maharam-type representation theorems for positive projections on Dedekind complete vector lattices. In the approach to these results the theory off-algebras plays a crucial role.

Keywords

Crucial Role General Theory Fourier Analysis Operator Theory Potential Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aliprantis, C. D., Burkinshaw, O. 1985Positive OperatorsAcademic PressOrlandoGoogle Scholar
  2. 2.
    Dodds, P. G., Huijsmans, C. B., Pagter, B. 1990Characterizations of conditional expectation-type operatorsPac. J. Math.1415577Google Scholar
  3. 3.
    Huijsmans, C. B., Pagter, B. 1984Subalgebras and Riesz subspaces of an f-algebraProc. London Math. Soc.48161174Google Scholar
  4. 4.
    Huijsmans, C. B., Pagter, B. 1986Averaging operators and positive contractive projectionsJ. Math. Analysis and Applications113163184CrossRefGoogle Scholar
  5. 5.
    Kusraev, A. G. 2000Dominated OperatorsKluwer Academic PublishersDordrechtMath. and Its Appl., Vol. 519Google Scholar
  6. 6.
    Luxemburg, W. A. J.: The work of Dorothy Maharam on kernel representations of linear operators, in: Measure and Measurable Dynamics (Rochester, NY, 1987), Am. Math. Soc., Providence, RI, 1989, pp. 177–183.Google Scholar
  7. 7.
    Luxemburg, W. A. J., Masterson, J. J. 1967An extension of the concept of the order dual of a Riesz spaceCan. J. Math.19488498Google Scholar
  8. 8.
    Luxemburg, W. A. J., Pagter, B. 2002Maharam extensions of positive operators and f–modulesPositivity6147190CrossRefGoogle Scholar
  9. 9.
    Luxemburg, W. A. J. and de Pagter, B.: Representations of positive projections II, Positivity, to appear.Google Scholar
  10. 10.
    Luxemburg, W. A. J., Zaanen, A. C. 1971Riesz Spaces INorth-HollandAmsterdamGoogle Scholar
  11. 11.
    Maharam, D. 1949The representation of abstract measure functionsTrans. Am. Math. Soc.65279330Google Scholar
  12. 12.
    Monk, J. D.Bonnet, R. eds. 1989Handbook of Boolean AlgebrasNorth-HollandAmsterdamVol. 3Google Scholar
  13. 13.
    Meyer-Nieberg, P. 1991Banach LatticesSpringer-VerlagBerlin–Heidelberg–New YorkGoogle Scholar
  14. 14.
    Nakano, H. 1950Modern Spectral TheoryMaruzenTokyoGoogle Scholar
  15. 15.
    Roman, Sikorski 1969Boolean Algebras3Springer-VerlagNew YorkGoogle Scholar
  16. 16.
    Zaanen, A. C. 1983Riesz Spaces IINorth-HollandAmsterdam–LondonGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • W. A. J. Luxemburg
    • 1
  • B. De Pagter
    • 2
  1. 1.MathematicsCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of MathematicsDelft University of TechnologyDelftThe Netherlands

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