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  • An extension of Lomonosov's techniques to non-compact operators
    Simonič, Aleksander
    The aim of this work is to generalize Lomonosov;s techniques in order to apply them to a wider class of not necessarily compact operators. We start by establishing a connection between the existence ... of invariant subspaces and density of what we define as the associated Lomonosov space in a certain function space. On a Hilbert space, approximation with Lomonosov functions results in an extended version of Burnside's theorem. An application of this theorem to the algebra generated by an essentially self-adjoint operator ▫$A$▫ yields the existence of vector states on the space of all polynomials restricted to the essential spectrum of ▫$A$▫. Finally, the invariant subspace problem for compact perturbations of self-adjoint operators acting on a real Hilbert space is translated into an extreme problem and the solution is obtained upon differentiating certain real-valued functions at their extreme.
    Source: Transactions of the American Mathematical Society. - ISSN 0002-9947 (Let. 348, št. 3, 1996, str. 975-995)
    Type of material - article, component part
    Publish date - 1996
    Language - english
    COBISS.SI-ID - 6006873

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