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The class of b-limited operators

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Abstract

We introduce a new class of operators that we call b-limited operators. Properties of b-limited operators, the relationship between the b-limited operators and various classes of operators are studied.

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References

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

    Book  Google Scholar 

  2. S. Alpay, B. Altin and C. Tonyali, On property (b) of vector lattices, Positivity, 7 (2003), 135–139.

    Article  MathSciNet  Google Scholar 

  3. B. Aqzzouz and J. Hmichane, The class of b-AM-compact operators, Quaestions Mathematicae, 36 (2013), doi: 10.2989/16073606.2013.805869.

  4. J. Bourgain and J. Diestel, Limited operators and strict cosingularity, Math. Nachrichten, 119 (1984), 55–58.

    Article  MathSciNet  Google Scholar 

  5. N. Cheng and Z. L. Chen, b-AM-compact operators on Banach lattice, Chinese J. Eng. Math., 27 (2010), 753–756.

    MathSciNet  MATH  Google Scholar 

  6. J. X. Chen, Z. L. Chen and G. X. Ji, Domination by positive weak* Dunford-Pettis operators on Banach lattices, arXiv (2013), arXiv: 1311.2808.

  7. P. G. Dodds, o-weakly compact mappings of Riesz spaces, Trans. Amer. Math. Soc., 214 (1975), 389–402.

    MathSciNet  MATH  Google Scholar 

  8. P. G. Dodds and D. H. Fremlin, Compact operators on Banach lattices, Israel J. Math., 34 (1979), 287–320.

    Article  MathSciNet  Google Scholar 

  9. A. El Kaddouri and M. Moussa, About the class of ordered limited operators, Acta Universitatis Carolinae. Mathematica et Physica, 54 (2013), no. 1.

    MathSciNet  MATH  Google Scholar 

  10. N. Machrafi, A. Elbour and M. Moussa, Some characterizations of almost limited sets and applications, arXiv (2013), arXiv: 1312.2770.

  11. M. Salimi and S. M. Moshtaghioun, The Gelfand-Phillips property in closed subspaces of some operator spaces, Banach J. Math. Anal., 5 (2011), 84–92.

    Article  MathSciNet  Google Scholar 

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Correspondence to Abdelmonaim El Kaddouri.

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Communicated by L. Kérchy

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El Kaddouri, A., El Fahri, K. & Moussa, M. The class of b-limited operators. ActaSci.Math. 82, 165–173 (2016). https://doi.org/10.14232/actasm-014-570-2

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  • DOI: https://doi.org/10.14232/actasm-014-570-2

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