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  • Moment problems for operator polynomials
    Cimprič, Jaka ; Zalar, Aljaž
    Haviland's theorem states that given a closed subset ▫$K$▫ in ▫$\mathbb{R}^{n}$▫, each functional ▫$L:\mathbb{R}[\underline x] \to \mathbb{R}$▫ positive on ▫$\text{Pos}(K) := \{ p \in ... \mathbb{R}[\underline x] |p|_K \ge 0\}$▫ admits an integral representation by a positive Borel measure [E. K. Haviland, Am. J. Math. 57, 562--568 (1935)]. Schmüdgen 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 [K. Schmüdgen, Math. Ann. 289, No.~2, 203--206 (1991)]. Further, he showed that the compactness of ▫$K$▫ is equivalent to the archimedianity of ▫$T$▫. The aim of the present paper is to extend these results from functionals on the usual real polynomials to operators mapping from the real matrix or operator polynomials into ▫$\mathbb{R}, M_{n}(\mathbb{R})$▫ or ▫$B(\mathcal{K})$▫.
    Vir: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 401, iss. 1, 2013, str. 307-316)
    Vrsta gradiva - članek, sestavni del
    Leto - 2013
    Jezik - angleški
    COBISS.SI-ID - 16602201

    Povezava(-e):

    http://dx.doi.org/10.1016/j.jmaa.2012.12.027

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