Bi-extensions of Closed Symmetric Operators

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


In this chapter we introduce and consider a new type of extensions of a given symmetric operator with its exit into the triplets of Hilbert spaces. These new extensions are called bi-extensions. We present a complete description and parameterizations of these bi-extensions. Special attention is paid to so-called twice self-adjoint (t-self-adjoint ) bi-extensions that will play an important role in the remaining part of this text.


Adjoint Operator Symmetric Operator Linear Manifold Bijective Correspondence Unitary Extension 
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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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