The oτ-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces

2021/05/05 by Alpay, Safak, Emelyanov, Eduard, Gorokhova, Svetlana · 1 citation
#2020: 46A40 #46B42 #47L05 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2105.01810

Abstract

We investigate the oτ-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the KB 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 by

• On Levi operators between normed and vector lattices

Related

• On Levi operators between normed and vector lattices
• uτ-continuous operators on locally solid vector lattices
• Compact-Like Operators in Vector Lattices Normed by Locally Solid Lattices
• On KB and Levi operators in Banach lattices
• Automatic boundedness of some operators between ordered and topological vector spaces