On the adjoint of a symmetric operator

Jussi Behrndt, Matthias Langer

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


In general it is a non-trivial task to determine the adjoint S* of an unbounded symmetric operator S in a Hilbert or Krein space. We propose a method to specify S* explicitly which makes use of two boundary mappings that satisfy an abstract Green's identity and a surjectivity condition, and give rise to a self-adjoint extension of S. We show for various concrete examples how convenient and easily applicable this technique is.
Original languageEnglish
Pages (from-to)563-580
Number of pages18
JournalJournal of the London Mathematical Society
Issue number3
Early online date15 Sept 2010
Publication statusPublished - 2010


  • symmetric operator
  • adjoint
  • self-adjoint extension
  • boundary mappings
  • Green's identity
  • surjectivity condition


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