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

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Alpay S., Emelyanov E., Gorokhova S.

RESULTS IN MATHEMATICS, vol.77, no.3, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 77 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1007/s00025-022-01650-3
  • Journal Name: RESULTS IN MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Topological vector space, locally solid lattice, Banach lattice, order convergence, domination property, adjoint operator, BANACH-LATTICES, UO-CONVERGENCE, DUNFORD-PETTIS, COMPACT
  • Middle East Technical University Affiliated: Yes

Abstract

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.