THE L-P SPACE OF A POSITIVE-DEFINITE MATRIX OF MEASURES AND DENSITY OF MATRIX POLYNOMIALS IN L-1

Authors
DURAN AJ LOPEZRODRIGUEZ P
Citation
Aj. Duran et P. Lopezrodriguez, THE L-P SPACE OF A POSITIVE-DEFINITE MATRIX OF MEASURES AND DENSITY OF MATRIX POLYNOMIALS IN L-1, Journal of approximation theory, 90(2), 1997, pp. 299-318
Citations number
21
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Journal of approximation theory → ACNP
ISSN journal
00219045
Volume
90
Issue
2
Year of publication
1997
Pages
299 - 318
Database
ISI
SICI code
0021-9045(1997)90:2<299:TLSOAP>2.0.ZU;2-L
Abstract
In this paper we study the space L-p(mu), 1 less than or equal to p le ss 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 vagu e topology, and we give a density result for L-1(mu) which is an exten sion to the matrix case of the classical result for scalar polynomials and positive measures due to Naimark. (C) 1997 Academic Press.