Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The nonproper dissipative extensions of a dual pair


Author: Christoph Fischbacher
Journal: Trans. Amer. Math. Soc. 370 (2018), 8895-8920
MSC (2010): Primary 47B44, 47A20; Secondary 47E05
DOI: https://doi.org/10.1090/tran/7511
Published electronically: September 5, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider dissipative operators $ A$ of the form $ A=S+iV$, where both $ S$ and $ V\geq 0$ are assumed to be symmetric, but neither of them needs to be (essentially) self-adjoint. After a brief discussion of the relation of the operators $ S\pm iV$ to dual pairs with the so-called common core property, we present a necessary and sufficient condition for any extension of $ A$ with domain contained in $ \mathcal {D}((S-iV)^*)$ to be dissipative. We will discuss several special situations in which this condition can be expressed in a particularly nice form--accessible to direct computations. Examples involving ordinary differential operators are given.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 47B44, 47A20, 47E05

Retrieve articles in all journals with MSC (2010): 47B44, 47A20, 47E05


Additional Information

Christoph Fischbacher
Affiliation: Department of Mathematics, The University of Alabama, Birmingham, Alabama 35294
Email: cfischb@uab.edu

DOI: https://doi.org/10.1090/tran/7511
Received by editor(s): June 13, 2017
Received by editor(s) in revised form: October 26, 2017
Published electronically: September 5, 2018
Additional Notes: The author is indebted to the UK Engineering and Physical Sciences Research Council (Doctoral Training Grant Ref. EP/K50306X/1).
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society