Mousavi Amiri, Masoumeh; Haghnejad Azar, Kazem Some notes on \(b\)-weakly compact operators. (English) Zbl 1501.47060 Bull. Iran. Math. Soc. 46, No. 5, 1533-1538 (2020). Summary: The main aim of this paper is studying the family \(W_b(E,F)\) of \(b\)-weakly compact operators between two Banach lattices. For an order dense sublattice \(G\) of a vector lattice \(E\), if \(T:G\rightarrow F\) is a \(b\)-weakly compact operator between two Banach lattices, then \(T\in W_b(E,F)\) whenever the norm of \(E\) is order continuous and \(T:E\rightarrow F\) is a positive operator. We also investigate the relationship between \(W_b(E,F)\) and some other classes of operators like \(L^{(1)}_c(E,F)\) and \(L^{(2)}_c(E,F)\). Cited in 1 Document MSC: 47B60 Linear operators on ordered spaces 46B42 Banach lattices 47B07 Linear operators defined by compactness properties Keywords:Banach lattice; order continuous norm; \(b\)-weakly compact operator PDFBibTeX XMLCite \textit{M. Mousavi Amiri} and \textit{K. Haghnejad Azar}, Bull. Iran. Math. Soc. 46, No. 5, 1533--1538 (2020; Zbl 1501.47060) Full Text: DOI References: [1] Abramovich, Y.; Sirotkin, G., On order convergence of nets, Positivity, 9, 287-292 (2005) · Zbl 1110.46002 · doi:10.1007/s11117-004-7543-x [2] Aliprantis, CD; Burkinshaw, O., Positive Operators (2006), Berlin: Springer, Berlin · Zbl 1098.47001 [3] Alpay, S.; Altin, B.; Tonyali, C., On property (b) of vector lattices, Positivity, 7, 135-139 (2003) · Zbl 1036.46018 · doi:10.1023/A:1025840528211 [4] Alpay, S.; Altin, B.; Tonyali, C., A note on Riesz spaces with property-b, Czechoslovak Math. J., 56, 765-772 (2006) · Zbl 1164.46310 · doi:10.1007/s10587-006-0054-0 [5] Alpay, S.; Altin, B., A note on \(b\)-weakly compact operators, Positivity, 11, 575-582 (2007) · Zbl 1137.47028 · doi:10.1007/s11117-007-2110-x [6] Alpay, S.; Altin, B., On Riesz spaces with \(b\)-property and \(b\)-weakly compact operators, Vladikavkaz. Mat. Zh., 11, 19-26 (2009) · Zbl 1324.46010 [7] Aqzzouz, B.; Elbour, A., On the weak compactness of \(b\)-weakly compact operators, Positivity, 14, 75-81 (2010) · Zbl 1198.47034 · doi:10.1007/s11117-009-0006-7 [8] Aqzzouz, B.; Moussa, M.; Hmichane, J., Some Characterizations of \(b\)-weakly compact operators, Math. Rep., 62, 315-324 (2010) · Zbl 1235.47019 [9] Gao, N.; Xanthos, F., Unbounded order convergence and application to martingales without probability, J. Math. Anal. Appl., 415, 931-947 (2014) · Zbl 1351.60053 · doi:10.1016/j.jmaa.2014.01.078 [10] Meyer-Nieberg, P., Banach Lattices, Universitex (1991), Berlin: Springer, Berlin · Zbl 0743.46015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.