Spaces of \(u\tau\)-Dunford-Pettis and \(u\tau\)-compact operators on locally solid vector lattices. (English) Zbl 1474.46007

Summary: Suppose \(X\) is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on \(X\). In this paper, we consider some situations under which these classes of bounded operators form locally solid vector lattices. In addition, we generalize some notions of \(uaw\)-Dunford-Pettis operators and \(uaw\)-compact operators defined on a Banach lattice to general theme of locally solid vector lattices. With the aid of appropriate topologies, we investigate some relations between topological and lattice structures of these operators. In particular, we characterize those spaces for which these concepts of operators and the corresponding classes of bounded ones coincide.


46A40 Ordered topological linear spaces, vector lattices
47B60 Linear operators on ordered spaces
46B40 Ordered normed spaces
47B07 Linear operators defined by compactness properties
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