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, cilt.77, sa.3, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 77 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s00025-022-01650-3
  • Dergi Adı: RESULTS IN MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Topological vector space, locally solid lattice, Banach lattice, order convergence, domination property, adjoint operator, BANACH-LATTICES, UO-CONVERGENCE, DUNFORD-PETTIS, COMPACT
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.