Self-adjoint extensions of symmetric operators

  • Joachim Weidmann
Part of the Graduate Texts in Mathematics book series (GTM, volume 68)


In Sections 5.4 and 5.5 we have already learned that certain symmetric operators (the semi-bounded and continuously invertible ones) possess self-adjoint extensions. The question of whether all (or which) symmetric operators have self-adjoint extensions could not be answered there. The key to our studies was the fact that λ — T was continuously invertible for some λ ∈ ℝ; however, this is not always the case. In this chapter we develop the von Neumann extension theory, which completely answers this question. Moreover, we shall prove certain theorems about the spectra of all self-adjoint extensions of a symmetric operator.


Real Hilbert Space Symmetric Operator Analytic Vector Complex Hilbert Space Isometric Mapping 
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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • Joachim Weidmann
    • 1
  1. 1.Institut für Angewandte MathematikMathematisches Seminar der Johann-Wolfgang-Goethe-Universität6 Frankfurt a. M.Federal Republic of Germany

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