Journal
ISRAEL JOURNAL OF MATHEMATICS
Volume 183, Issue 1, Pages 445-474Publisher
HEBREW UNIV MAGNES PRESS
DOI: 10.1007/s11856-011-0056-y
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We consider the problem of determining the closure (M) over bar of a quadratic module M in a commutative R-algebra with respect to the finest locally convex topology. This is of interest in deciding when the moment problem is solvable [28] [29] and in analyzing algorithms for polynomial optimization involving semidefinite programming [12]. The closure of a semiordering is also considered, and it is shown that the space Y-M consisting of all semiorderings lying over M plays an important role in understanding the closure of M. The result of Schmudgen for preorderings in [29] is strengthened and extended to quadratic modules. The extended result is used to construct an example of a non-archimedean quadratic module describing a compact semialgebraic set that has the strong moment property. The same result is used to obtain a recursive description of (M) over bar which is valid in many cases.
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