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Alpay, Safak; Emelyanov, Eduard; Gorokhova, Svetlana

\(o\tau \)-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces. (English) Zbl 07517404

Result. Math. 77, No. 3, Paper No. 117, 25 p. (2022).
Summary: We investigate \(o\tau \)-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the Kantorovich-Banach operators between locally solid lattices and topological vector spaces; and the Levi operators from locally solid lattices to vector lattices. The main idea of operator versions of notions related to vector lattices lies in redistributing topological and order properties of a topological vector lattice between the domain and range of an operator under investigation. Domination properties for these classes of operators are studied.

Cited in 2 Documents

MSC:

47B60 Linear operators on ordered spaces
46A40 Ordered topological linear spaces, vector lattices
46B42 Banach lattices
47L05 Linear spaces of operators

Keywords:

topological vector space; locally solid lattice; Banach lattice; order convergence; domination property; adjoint operator
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\textit{S. Alpay} et al., Result. Math. 77, No. 3, Paper No. 117, 25 p. (2022; Zbl 07517404)
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