Electronic Theses and Dissertations

Date of Award

2017

Document Type

Dissertation

Degree Name

Ph.D. in Mathematics

Department

Mathematics

First Advisor

Gerard Buskes

Second Advisor

Sandra M. Spiroff

Third Advisor

Qingying Bu

Relational Format

dissertation/thesis

Abstract

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.

Included in

Mathematics Commons

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