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Domination problem for AM-compact abstract Uryson operators

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Abstract

The Boolean algebra of fragments of a positive abstract Uryson operator recently was described in M. Pliev (Positivity, doi:10.1007/s11117-016-0401-9, 2016). Using this result, we prove a theorem of domination for AM-compact positive abstract Uryson operators from a Dedekind complete vector lattice E to a Banach lattice F with an order continuous norm.

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References

  1. Abasov N., Pliev M.: Order properties of the space of dominated Uryson operators. Int. Journal of Math. Analysis 9, 2211–2219 (2015)

    Article  Google Scholar 

  2. C. D. Aliprantis and O. Burkinshaw, Positive Operators, Springer, Dordrecht, 2006.

  3. Ben Amor M.A., Pliev M.: Laterally continuous part of an abstract Uryson operator. Int. J. of Math. Analysis 7, 2853–2860 (2013)

    Article  MathSciNet  Google Scholar 

  4. P. G. Dodds and D. H. Fremlin, Compact Operators in Banach Lattices, Israel J. Math. 34 (1979), 287–320.

  5. A. V. Gumenchuk, M. A. Pliev, and M. M. Popov, Extensions of orthogonally additive operators, Mat. Stud. 41 (2014), 214–219.

  6. A. G. Kusraev, Dominated Operators, Kluwer Acad. Publ., Dordrecht–Boston–London, 2000.

  7. Mazón J. M., Segura de León S.: Order bounded ortogonally additive operators. Rev. Roumane Math. Pures Appl. 35, 329– (1990)

    MATH  Google Scholar 

  8. J. M. Mazón and S. Segura de León, Uryson operators, Rev. Roumane Math. Pures Appl. 35 (1990), 431–449.

  9. A. G. Kusraev and M. A. Pliev, Orthogonally additive operators on lattice-normed spaces, Vladikavkaz Math. J. 3 (1999), 33–43.

  10. Kusraev A. G., Pliev M. A.: Weak integral representation of the dominated orthogonally additive operators. Vladikavkaz Math. J. 4, 22–39 (1999)

    MathSciNet  MATH  Google Scholar 

  11. V. Mykhaylyuk, M. Pliev, M. Popov, and O. Sobchuk, Dividing measures and narrow operators, Studia Math. 231 (2015), 97–116.

  12. M. Pliev, Domination problem for narrow orthogonally additive operators, Positivity (2016). doi:10.1007/s11117-016-0401-9.

  13. Pliev M., Popov M.: Narrow orthogonally additive operators. Positivity 18, 641–667 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pliev M., Popov M.: Dominated Uryson operators. Int. J. of Math. Analysis 8, 1051–1059 (2014)

    Article  Google Scholar 

  15. M. A. Pliev and M. R. Weber, Disjointness and order projections in the vector lattices of abstract Uryson operators, Positivity, doi:10.1007/s11117-015-0381-1.

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Authors and Affiliations

  1. Voronezh State University, Universitetskaya pl., Voronezh, 394006, Russia

    Vladimir Orlov & Dmitry Rode

  2. Southern Mathematical Institute of the Russian Academy of Sciences, str. Markusa 22, Vladikavkaz, 362027, Russia

    Marat Pliev

  3. Peoples’ Friendship University of Russia, 117198, M.-Maklaya str., 6, Moscow, Russia

    Marat Pliev

Authors
  1. Vladimir Orlov
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  2. Marat Pliev
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  3. Dmitry Rode
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Correspondence to Marat Pliev.

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Orlov, V., Pliev, M. & Rode, D. Domination problem for AM-compact abstract Uryson operators. Arch. Math. 107, 543–552 (2016). https://doi.org/10.1007/s00013-016-0937-8

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  • DOI: https://doi.org/10.1007/s00013-016-0937-8

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