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)

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Official URL: http://dx.doi.org/10.1007/s00020-016-2310-5

Abstract

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
Institutional Unit:	Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences
Former Institutional Unit:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Ian Wood
Date Deposited:	09 Oct 2016 15:36 UTC
Last Modified:	20 May 2025 11:38 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/57819 (The current URI for this page, for reference purposes)

University of Kent Author Information

Fischbacher, Christoph.

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Naboko, Serguei.

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Wood, Ian.

Creator's ORCID:	https://orcid.org/0000-0001-7181-7075
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