Some notes on orthogonally additive polynomials
24 Mar 2022We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using separately two polynomial identities of Kusraeva involving the root mean power and the geometric mean. Furthermore, it is shown that a polynomial on a vector lattice is orthogonally additive whenever it is orthogonally additive on the positive cone. These results improve recent characterizations of bounded orthogonally additive polynomials by G. Buskes and the author.
| Authors: | Schwanke, Christopher |
| Institution: | University of Pretoria |
| Keywords: | Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power, Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power |