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Some notes on \(b\)-weakly compact operators. (English) Zbl 1501.47060

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 \(L^{(2)}_c(E,F)\).

MSC:

47B60 Linear operators on ordered spaces
46B42 Banach lattices
47B07 Linear operators defined by compactness properties
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References:

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