Orthosymmetric Maps And Polynomial Valuations

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.

Name thesis:degree_name

Ph.D. in Mathematics

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2017

Author dc:creator

• Roberts, Stephan Christopher

Contributors dc:contributor

• Gerard Buskes
• Sandra Spiroff
• Qingying Bu

• Functional Analysis
• Orthogonally Additive
• Orthosymmetric
• Riesz Spaces
• Vector Lattices
• Mathematics

Repository record dc:identifier

https://egrove.olemiss.edu/etd/680

OAI identifier oai:identifier

oai:egrove.olemiss.edu:etd-1679