The Proper Dissipative Extensions of a Dual Pair

Academic Article


  • © 2016, Springer International Publishing. Let A and (- A~) be dissipative operators on a Hilbert space H and let (A, A~) form a dual pair, i.e. A⊂ A~ ∗ , resp. A~ ⊂ A ∗ . We present a method of determining the proper dissipative extensions A^ of this dual pair, i.e. A⊂ A^ ⊂ A~ ∗ provided that D(A) ∩ D(A~) is dense in H. Applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are discussed. Finally, we investigate the stability of the numerical range of the different dissipative extensions.
  • Digital Object Identifier (doi)

    Author List

  • Fischbacher C; Naboko S; Wood I
  • Start Page

  • 573
  • End Page

  • 599
  • Volume

  • 85
  • Issue

  • 4