Abstract
We consider a continuous operator T: E → X where E is a Banach lattice and X is a Banach space. We characterize the b-weak compactness of T in terms of its mapping properties.
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References
C.D. Aliprantis, O. Burkinshaw, Positive Operators, Academic Press, New York and London (1985).
C.D. Aliprantis, O. Burkinshaw, Locally Solid Riesz Spaces, Academic Press, New York (1978).
Ş. Alpay, B. Altın, C. Tonyalı, On property (b) of vector lattices, Positivity, 7 (2003), 135–139.
Ş. Alpay, B. Altın, C. Tonyalı, A note on Riesz spaces with property-b, Czech Math. J., 131 (2006), 765–772.
B. Altın, On Banach lattices with Levi norms, Proc. Am. Math. Soc., 135(4) (2007), 1059–1063.
B. Altın, On b-weakly compact operators on Banach lattices, Taiwanese J. Math. 11(1) (2007), 143–150.
Z.L. Chen, A.W. Wickstead, Vector lattices of weakly compact operators on Banach lattices, Trans. Am. Math. Soc., 352, (2000), 397–412.
P.G. Dodds, o-weakly compact mappings of Riesz spaces, Trans. Am. Math. Soc., 214 (1975), 389–402.
P. Meyer-Nieberg, Banach Lattices Universitext, Springer, Berlin (1991).
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Alpay, Ş., Altın, B. A Note on b-Weakly Compact Operators. Positivity 11, 575–582 (2007). https://doi.org/10.1007/s11117-007-2110-x
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DOI: https://doi.org/10.1007/s11117-007-2110-x