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An extension of Lomonosov's techniques to non-compact operatorsSimonič, AleksanderThe 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 partPublish date - 1996Language - englishCOBISS.SI-ID - 6006873
Author
Simonič, Aleksander
Topics
matematika |
funkcionalna analiza |
operatorska teorija |
Hilbertov prostor |
linearni operatorji |
nekompaktni operatorji |
invariantni podprostori |
mathematics |
functional analysis |
operator theory |
Hilbert space |
linear operators |
non-compact operators |
invariant subspace
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source: Transactions of the American Mathematical Society. - ISSN 0002-9947 (Let. 348, št. 3, 1996, str. 975-995)
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Simonič, Aleksander | 07078 |
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