  In this paper we provide a way to construct new moment sequences from a given
moment sequence. An operator based on multivariate positive polynomials is
applied to get the new moment sequences. A class of new sequences is
corresponding to a unique symmetric polynomial; if this polynomial is positive,
then the new sequence becomes again a moment sequence. We will see for instance
that a new sequence generated from minors of a Hankel matrix of a Stieltjes
moment sequence is also a Stieltjes moment sequence.
