Opuscula Math. 41, no. 3 (2021), 381-393
https://doi.org/10.7494/OpMath.2021.41.3.381

 
Opuscula Mathematica

Extensions of dissipative operators with closable imaginary part

Christoph Fischbacher

Abstract. Given a dissipative operator \(A\) on a complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) is closable, we give a necessary and sufficient condition for an extension of \(A\) to still be dissipative. As applications, we describe all maximally accretive extensions of strictly positive symmetric operators and all maximally dissipative extensions of a highly singular first-order operator on the interval.

Keywords: extension theory, dissipative operators, ordinary differential operators.

Mathematics Subject Classification: 34L99, 47H06.

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  • Communicated by Andrei Shkalikov.
  • Received: 2020-12-01.
  • Accepted: 2021-01-23.
  • Published online: 2021-04-19.
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Cite this article as:
Christoph Fischbacher, Extensions of dissipative operators with closable imaginary part, Opuscula Math. 41, no. 3 (2021), 381-393, https://doi.org/10.7494/OpMath.2021.41.3.381

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