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The Proper Dissipative Extensions of a Dual Pair

Fischbacher, Christoph, Naboko, Serguei, Wood, Ian (2016) The Proper Dissipative Extensions of a Dual Pair. Integral Equations and Operator Theory, 85 (4). pp. 573-599. ISSN 0378-620X. (doi:10.1007/s00020-016-2310-5) (KAR id:57819)


Let A and B be dissipative operators on a Hilbert space H and let (A,B) form a dual pair, i.e. A ? B*, resp. B ? A*. We present a method of determining the proper dissipative extensions C of this dual pair, i.e. A ? C ? B* provided that D(A) ? D(B) 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.

Item Type: Article
DOI/Identification number: 10.1007/s00020-016-2310-5
Uncontrolled keywords: Dissipative operators, Operator extensions, Dual pairs
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Ian Wood
Date Deposited: 09 Oct 2016 15:36 UTC
Last Modified: 11 Jul 2019 13:20 UTC
Resource URI: (The current URI for this page, for reference purposes)
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