Date of Award
Ph.D. in Mathematics
Sandra M. Spiroff
We present a characterization of orthogonally additive polynomials on vector lattices as orthosymmetric multilinear maps. Our proof avoids partitionaly orthosymmetric maps and results that represent orthogonally additive polynomials as linear maps on a power. We also prove band characterizations for order bounded polynomial valuations and for order continuous polynomials of order bounded variation. Finally, we use polynomial valuations to prove that a certain restriction of the Arens extension of a bounded orthosymmetric multilinear map is orthosymmetric.
Roberts, Stephan Christopher, "Orthosymmetric Maps And Polynomial Valuations" (2017). Electronic Theses and Dissertations. 680.