The [formula omitted]pSpace of a Positive Definite Matrix of Measures and Density of Matrix Polynomials inL1

Abstract

In this paper we study the space Lp(μ), 1⩽p⩽+∞,μbeing a positive definite matrix of measures. We prove that the set of all positive definite matrices of measures having the same moments as those ofμis compact in the vague topology, and we give a density result for L1(μ) which is an extension to the matrix case of the classical result for scalar polynomials and positive measures due to Naimark.