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Positivity

, Volume 9, Issue 3, pp 491–499 | Cite as

Convex Solid Subsets of L0(X, μ)

  • Anton R. SchepEmail author
Article

Abstract

If AL0(X, μ) is a convex solid subset of L0(X, μ), then there exist disjoint X0 and X1 with X = X0X1 such that A| X_0 is dense in L0(X0, μ) and A|X_1 is bounded in measure in L0(X1, μ).

Keywords

Fourier Analysis Operator Theory Potential Theory Convex Solid Solid Subset 
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.
    Abramovitch, Y.A. and Aliprantis, C.D.: An invitation to operator theory, Graduate Stud. Math. 50, AMS (2002).Google Scholar
  2. 2.
    Kalton, N.J., Verbitsky, I. E. 1999Nonlinear equations and weighted norm inequalitiesTrans. AMS35134413497CrossRefGoogle Scholar
  3. 3.
    Maurey, B.: Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces Lp, Astérisque 11, 1974.Google Scholar
  4. 4.
    Nikišin, E.M. 1970Resonance theorems and superlinear operatorsRuss. Math. Surv.25124187Google Scholar
  5. 5.
    Schep, A.R. 1984Factorization of positive multilinear mapsIllin J. Math28579591Google Scholar
  6. 6.
    Zaanen, A.C.: Integration, North-Holland, 1967.Google Scholar
  7. 7.
    Zaanen, A.C.: Riesz Spaces II, North-Holland, 1983.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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