Moment problems for operator polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:401

Article

Cimpric, Jaka¹  Zalar, Aljaz¹ 

[1] Univ Ljubljana, Fac Math & Phys, Dept Math, SI-1000 Ljubljana, Slovenia

关键词: Moment problems;    Operator-valued measures;    Operator polynomials;    Real algebraic geometry;   

DOI  :  10.1016/j.jmaa.2012.12.027

来源: Elsevier

【 摘 要 】

Haviland's theorem states that given a closed subset K in R-n, each functional L : R[x] -> R positive on Pos(K) := {p is an element of R[x]vertical bar p vertical bar(K) >= 0} admits an integral representation by a positive Borel measure. Schmtidgen proved that in the case of compact semialgebraic set K it suffices to check positivity of L on a preordering T, having K as the non-negativity set. Further he showed that the compactness of K is equivalent to the archimedianity of T. The aim of this paper is to extend these results from functionals on the usual real polynomials to operators mapping from the real matrix or operator polynomials into R, M-n(R) or B(K). (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free