Support sets of nonlinear functionals

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© 2019 American Mathematical Society. Any Dedekind complete Banach lattice E with a quasi-interior point e is lattice isomorphic to a space of continuous, extended real-valued functions defined on a compact Hausdorff space X. An orthogonally additive, continuous, monotonic, and subhomogeneous nonlinear functional T: E → R is studied. In this case, the concept of integration is no longer valid. However, a measure μ related to the nonlinear operator T can be constructed as well as an associated linear operator. This measure and linear operator can be used to study nonlinear functionals. It is shown that this associated linear operator is unique and results regarding support sets will be presented.

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Contemporary Mathematics

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