Pure states, nonnegative polynomials and sums of squares

Understand

In recent years, much work has been devoted to a systematic study of polynomial identities certifying strict or non-strict positivity of a polynomial on a basic closed semialgebraic set.

• The interest in such identities originates not least from their importance in polynomial optimization.
• The majority of the important results requires the archimedean condition, which implies that the semialgebraic set has to be compact.
• This paper introduces the technique of pure states into commutative algebra.