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Positivity

, Volume 9, Issue 3, pp 397–399 | Cite as

A Dedekind σ-Complete Banach Lattice into which all Bounded Operators are Regular

  • Z. ErcanEmail author
  • S. Onal
Article

Abstract

We give an answer to a question of Abramovich–Wickstead asked in [Quart. J. Math. Oxford (2), 44 (1993), 257–270] under the axiom ‘measurable cardinal exists’.

Keywords

BIR-space Banach lattices measurable cardinal 

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References

  1. 1.
    Abramovich, Y.A., Wickstead, A.W. 1993The regularity of order bounded operators into C(K) II, QuartJ. Math. Oxford(2)44257270Google Scholar
  2. 2.
    Abramovich, Y.A., Wickstead, A.W. 1997When Each Continuous Operator is RegularII. Indag. Math. (N.S.)8281294Google Scholar
  3. 3.
    Aliprantis, C.D., Burkinshaw, O. 1985Positive OperatorsAcademic PressNew York LondonGoogle Scholar
  4. 4.
    Hrbacek, K., Jech, T. 1984Introduction Set Theory2Marcel DekkerNew YorkGoogle Scholar
  5. 5.
    Jech, T.: Set Theory, Springer-Verlag, 2003.Google Scholar
  6. 6.
    Meyer-Nieberg, P.: Banach Lattices, Springer-Verlag, 1991.Google Scholar
  7. 7.
    Wickstead, A.W. 1990The Regularity of order bounded operators into C(K), QuartJ. Math. Oxford(2)41359368Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

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