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Some new results on the class of AM-compact operators

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Abstract

We establish some new necessary and sufficient conditions under which each regular operator is AM-compact if and only if its adjoint is AM-compact. Also, we give some consequences.

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References

  1. Aliprantis, C.D., Burkinshaw, O.: Positive operators. (Reprint of the 1985 original) Dordrecht: Springer (2006)

    MATH  Google Scholar 

  2. Aqzzouz, B., Nouira, R., Zraoula, L.: Compactness properties of operators dominated by AM-compact operators, Proc. Amer. Math. Soc., 135 (2007), 1151–1157

    Article  MATH  MathSciNet  Google Scholar 

  3. Aqzzouz, B., Nouira, R., Zraoula, L.: The duality problem for the class of AM-compact operators on Banach lattices, Canad.Math. Bull., 51 (2008), 15–20

    Article  MATH  MathSciNet  Google Scholar 

  4. Aqzzouz, B., Nouira, R., Zraoula, L.: On the duality problem of positive Dunford-Pettis operators on Banach lattices, Rend. Circ. Mat. Palermo, 57 (2008), 287–294

    Article  MATH  MathSciNet  Google Scholar 

  5. Aqzzouz, B., Elbour, A.: Some characterizations of compact operators on Banach lattices, Rend. Circ. Mat. Palermo, 57 (2008), 423–431

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen, Z.L., Wickstead, A.W.: Some applications of Rademacher sequences in Banach lattices, Positivity, 2 (1998), 171–191

    Article  MATH  MathSciNet  Google Scholar 

  7. Fremlin, D.H.: Riesz spaces with the order continuity property I, Proc. Cambr. Phil. Soc., 81 (1977), 31–42

    Article  MATH  MathSciNet  Google Scholar 

  8. Meyer-Nieberg, P.: Banach lattices. (Universitext) Berlin: Springer-Verlag (1991)

    MATH  Google Scholar 

  9. Wnuk, W.: A characterization of discrete Banach lattices with order continuous norms, Proc. Amer.Math. Soc., 104 (1988), 197–200

    MATH  MathSciNet  Google Scholar 

  10. Wnuk, W.: Banach lattices with order continuous norms. Warsaw: Polish Scientific Publishers (1999)

    MATH  Google Scholar 

  11. Zaanen, A.C.: Riesz spaces II. North Holland Publishing Company (1983)

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Correspondence to Belmesnaoui Aqzzouz.

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Aqzzouz, B., Elbour, A. Some new results on the class of AM-compact operators. Rend. Circ. Mat. Palermo 59, 267–275 (2010). https://doi.org/10.1007/s12215-010-0020-4

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  • DOI: https://doi.org/10.1007/s12215-010-0020-4

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