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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C. D. Aliprantis and O. Burkinshaw, Positive operators, Reprint of the 1985 original, Springer, Dordrecht, 2006.
S. Alpay, B. Altin and C. Tonyali, On property (b) of vector lattices, Positivity, 7 (2003), 135–139.
B. Aqzzouz and J. Hmichane, The class of b-AM-compact operators, Quaestions Mathematicae, 36 (2013), doi: 10.2989/16073606.2013.805869.
J. Bourgain and J. Diestel, Limited operators and strict cosingularity, Math. Nachrichten, 119 (1984), 55–58.
N. Cheng and Z. L. Chen, b-AM-compact operators on Banach lattice, Chinese J. Eng. Math., 27 (2010), 753–756.
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.
P. G. Dodds, o-weakly compact mappings of Riesz spaces, Trans. Amer. Math. Soc., 214 (1975), 389–402.
P. G. Dodds and D. H. Fremlin, Compact operators on Banach lattices, Israel J. Math., 34 (1979), 287–320.
A. El Kaddouri and M. Moussa, About the class of ordered limited operators, Acta Universitatis Carolinae. Mathematica et Physica, 54 (2013), no. 1.
N. Machrafi, A. Elbour and M. Moussa, Some characterizations of almost limited sets and applications, arXiv (2013), arXiv: 1312.2770.
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.
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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