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Canonical L-systems with Contractive and Accretive Operators

  • Yuri Arlinskii
  • Sergey Belyi
  • Eduard Tsekanovskii
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 217)

Abstract

In this chapter the Kreın classical theorem is extended to the case of quasiself-adjoint contractive extensions of symmetric contractions, and their complete parametrization is given. On its basis we present the solution of the Phillips-Kato restricted extension problem on existence and description of all proper maximal accretive and sectorial extensions of a densely-defined non-negative symmetric operator. The criterion in terms of the impedance function of an L-system for the state-space operator to be a contraction (or so-called θ-co-sectorial contraction) is obtained. We establish the conditions for a given Stieltjes and inverse Stieltjes function to be realized as an impedance function of some L-system. We also verify when the state-space operator of an L-system is maximal accretive or sectorial. The connections between the Friedrichs and Kre?in-von Neumann extensions and impedance function of L-systems are provided.

Keywords

Hilbert Space Symmetric Operator Impedance Function Accretive Operator Contractive Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Yuri Arlinskii
    • 1
  • Sergey Belyi
    • 2
  • Eduard Tsekanovskii
    • 3
  1. 1.Department of MathematicsEast Ukrainian National UniversityLuganskUkraine
  2. 2.Department of MathematicsTroy UniversityTroyUSA
  3. 3.Department of MathematicsNiagara UniversityLewistonUSA

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