o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces

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2022-06-01

Author

Alpay, Safak
Emelyanov, Eduard
Gorokhova, Svetlana

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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.

Subject Keywords

Topological vector space, locally solid lattice, Banach lattice, order convergence, domination property, adjoint operator, BANACH-LATTICES, UO-CONVERGENCE, DUNFORD-PETTIS, COMPACT

URI

https://hdl.handle.net/11511/97292

Journal

RESULTS IN MATHEMATICS

DOI

https://doi.org/10.1007/s00025-022-01650-3

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Department of Mathematics, Article

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Citation Formats

S. Alpay, E. Emelyanov, and S. Gorokhova, “o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces,” RESULTS IN MATHEMATICS, vol. 77, no. 3, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/97292.