Completely additive and \(C\)-compact operators in lattice-normed spaces

DOI10.1007/s43034-020-00058-wzbMath1501.47097OpenAlexW3011977715MaRDI QIDQ2192852

Nariman Abasov

Publication date: 21 August 2020

Published in: Annals of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s43034-020-00058-w

zbMATH Keywords

dominated operatorlattice-normed spaceorthogonally additive operatorcompletely additive operator

Mathematics Subject Classification ID

Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Ordered normed spaces (46B40)

Related Items

Orthogonally Additive Operators on Vector Lattices ⋮ Operators taking values in Lebesgue-Bochner spaces ⋮ Orthogonally bi-additive operators. II ⋮ On orthogonally additive operators in lattice-normed spaces ⋮ The Kalton and Rosenthal type decomposition of operators in Köthe-Bochner spaces ⋮ On a band generated by a disjointness preserving orthogonally additive operator ⋮ On compact orthogonally additive operators ⋮ On band preserving orthogonally additive operators ⋮ On orthogonally additive operators in Köthe-Bochner spaces ⋮ On orthogonally additive operators in \(C\)-complete vector lattices ⋮ Orthogonally biadditive operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Disjointness and order projections in the vector lattices of abstract Uryson operators
• Narrow operators on lattice-normed spaces
• Domination problem for \(AM\)-compact abstract Uryson operators
• Order unbounded orthogonally additive operators in vector lattices
• Compact-like operators in lattice-normed spaces
• Finite elements in some vector lattices of nonlinear operators
• Dominated orthogonally additive operators in lattice-normed spaces
• On extensions of some nonlinear maps in vector lattices
• Narrow and \(C\)-compact orthogonally additive operators in lattice-normed spaces
• On sums of narrow and compact operators
• Domination problem for narrow orthogonally additive operators
• A characterization of non-linear maps satisfying orthogonality properties
• Narrow orthogonally additive operators in lattice-normed spaces
• A factorization for orthogonally additive operators on Banach lattices
• Valuations on Banach Lattices