Associating linear and nonlinear operators
© 2017 Amerian Mathematial Soiety. 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 operator T: E → R is examined. In this case, the concept of integration is no longer valid, but a measure μ related to the nonlinear operator T is constructed. The linear operator associated with μ and other linear operators with similar properties are studied.
Stovall, J., & Feldman, W. (2017). Associating linear and nonlinear operators. Contemporary Mathematics. Retrieved from https://ir.una.edu/math_facpub/15