VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • On ▫$q$▫-normal operators and the quantum complex plane
    Cimprič, Jaka ; Savchuk, Yurii, 1983- ; Schmüdgen, Konrad
    For ▫$ q>0$▫ let▫ $ \mathcal{A}$▫ denote the unital ▫$\ast$▫-algebra with generator ▫$x$▫ and defining relation ▫$ xx^\ast = qx^{\ast}x$▫. Based on this algebra we study ▫$q$▫-normal operators and ... the complex ▫$q$▫-moment problem. Among other things, we prove a spectral theorem for ▫$q$▫-normal operators, a variant of Haviland's theorem and a strict Positivstellensatz for ▫$\mathcal{A}$▫. We also construct an example of a positive element of ▫$ \mathcal{A}$▫ which is not a sum of squares. It is used to prove the existence of a formally ▫$q$▫-normal operator which is not extendable to a ▫$q$▫-normal one in a larger Hilbert space and of a positive functional on ▫$\mathcal{A}$▫ which is not strongly positive.
    Vir: Transactions of the American Mathematical Society. - ISSN 0002-9947 (Vol. 366, no. 1, 2014, str. 135-158)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2014
    Jezik - angleški
    COBISS.SI-ID - 16921177

    Povezava(-e):

    http://dx.doi.org/10.1090/S0002-9947-2013-05733-9

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