Mathematische Zeitschrift

, Volume 255, Issue 3, pp 579–596

Strong majorization in a free ✱-algebra

  • J. William. Helton
  • Scott McCullough
  • Mihai Putinar

DOI: 10.1007/s00209-006-0032-0

Cite this article as:
Helton, J.W., McCullough, S. & Putinar, M. Math. Z. (2007) 255: 579. doi:10.1007/s00209-006-0032-0


We study, in the spirit of modern real algebra, the interplay between left ideals of the free ∗-algebra \(\mathbb F\) with n generators, and their suitably defined zero sets; and similarly between quadratic submodules of \(\mathbb F\) and their positivity sets.


PositivstellensatzNullstellensatzFree ∗-algebra

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • J. William. Helton
    • 1
  • Scott McCullough
    • 2
  • Mihai Putinar
    • 3
  1. 1.Department of MathematicsUniversity of California at San DiegoLa JollaUSA
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA
  3. 3.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA