Disjointness-preserving orthogonally additive operators in vector lattices

DOI10.1215/17358787-2018-0001zbMath1504.47087OpenAlexW2808617707WikidataQ129666869 ScholiaQ129666869MaRDI QIDQ1790178

Nariman Abasov, M. A. Pliev

Publication date: 2 October 2018

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bjma/1529114495

zbMATH Keywords

Boolean algebravector latticeabstract Urysohn operatordisjointness-preserving operatororthogonally additive nonlinear operatorUrysohn lattice homomorphism

Mathematics Subject Classification ID

Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Ordered topological linear spaces, vector lattices (46A40)

Related Items (14)

A Radon-Nikodym theorem for nonlinear functionals on Banach lattices ⋮ Band projections and decomposition of normal traces on von Neumann algebras ⋮ A factorization for orthogonally additive operators on Banach lattices ⋮ Nonlinear functionals on Banach lattices satisfying disjointness preserving properties ⋮ Some remarks on orthogonally additive operators ⋮ On orthogonally additive band operators and orthogonally additive disjointness preserving operators ⋮ Orthogonally bi-additive operators. II ⋮ Atomic operators in vector lattices ⋮ On \(C\)-compact orthogonally additive operators ⋮ On a band generated by a disjointness preserving orthogonally additive operator ⋮ On band preserving orthogonally additive operators ⋮ Orthogonally biadditive operators ⋮ Approximate \(\rho_\lambda^v\)-orthogonality and its preservation ⋮ The Radon-Nikodým Theorem for Disjointness Preserving Orthogonally Additive Operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On order bounded disjointness preserving operators
• Lattice preserving maps on lattices of continuous functions
• An alternative proof of a Radon-Nikodým theorem for lattice homomorphisms
• Domination problem for \(AM\)-compact abstract Uryson operators
• The components of a positive operator
• In the shadow of a positive operator
• Band decomposition for disjointness preserving operators
• Linear biseparating maps between spaces of vector-valued differentiable functions and automatic continuity
• Several order projectors generated by ideals of a vector lattice
• On extensions of some nonlinear maps in vector lattices
• Narrow orthogonally additive operators
• Extensions of orthogonally additive operators
• A characterization of non-linear maps satisfying orthogonality properties
• On the sum of narrow and finite-rank orthogonally additive operators
• Unbounded disjointness preserving linear functionals and operators
• Dividing measures and narrow operators
• Orthogonally additive holomorphic maps between C$^{*}$-algebras
• Inverses of disjointness preserving operators
• ORTHOGONALLY ADDITIVE POLYNOMIALS ON C*-ALGEBRAS
• Orthogonally additive holomorphic functions of bounded type over C(K)
• Characterizations of Disjointness preserving operators on vector-valued function spaces

This page was built for publication: Disjointness-preserving orthogonally additive operators in vector lattices