The L-p space of a positive definite matrix of measures and density of matrix polynomials in L-1

In this paper we study the space L-p(mu), 1 less than or equal to p less than or equal to + infinity, mu being a positive definite matrix of measures. We prove that the set of all positive definite matrices of measures having the same moments as those of mu is compact in the vague topology, and we give a density result for L-1(mu) which is an extension to the matrix case of the classical result for scalar polynomials and positive measures due to Naimark. (C) 1997 Academic Press.