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Archiv der Mathematik

, Volume 112, Issue 2, pp 181–190 | Cite as

Characterizing bounded orthogonally additive polynomials on vector lattices

  • G. BuskesEmail author
  • C. Schwanke
Article
  • 27 Downloads

Abstract

We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in Kusraeva (Vladikavkaz Math J 16(4):49–53, 2014) actually characterize them. Secondly, by employing complexifications of the unique symmetric multilinear maps associated with orthogonally additive polynomials, we derive new characterizing formulas.

Keywords

Vector lattice Orthogonally additive polynomial Geometric mean Root mean power Complexification 

Mathematics Subject Classification

46A40 

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Notes

Acknowledgements

This research was partially supported by the Claude Leon Foundation and by the DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (second author). Opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the CoE-MaSS.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MississippiUniversityUSA
  2. 2.Department of MathematicsLyon CollegeBatesvilleUSA

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