Quasi-self-adjoint Extensions

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


In this chapter we consider quasi-self-adjoint extensions of, generally speaking, non-densely defined symmetric operators and establish analogues of von Neumann’s and \({\rm Krasnoselski\breve{i}^\prime s}\) formulas in cases of direct and indirect decompositions of their domains. The quasi-self-adjoint bi-extensions and the so-called (*)- extensions (with exit into triplets of rigged Hilbert spaces) of symmetric operators will be introduced. We also present an analysis of these extensions together with their description and parametrization.


Uniqueness Theorem Symmetric Operator Linear Manifold Dissipative Operator Range Property 
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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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