Arlinskiĭ, Yury; Tretter, Christiane (2020). Everything is possible for the domain intersection ${\rm dom}\,T\cap{\rm dom}\,T*$. Advances in mathematics, 374, p. 107383. Elsevier 10.1016/j.aim.2020.107383
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In this paper we show that for the domain intersection
dom T \cap dom T^* of a closed linear operator and its Hilbert space adjoint everything is possible for very common classes of operators with nonempty resolvent set. Apart from the most striking case of a maximal sectorial operator with domT \cap dom T^*={0}, we construct classes of operators for which dim (domT \cap domT^*)=n \in \mathbb N_0; dim (domT \cap domT^*)=\infty and at the same time codim (domT \cap domT^*)=\infty; and codim (domT \cap domT^*)=n \in \mathbb N_0; the latter includes the case that domT \cap dom T^* is dense but no core of \mathcal T and T^* and the case dom T=dom T^* for nonnormal \mathcal T. We also show that all these possibilities may occur for operators \mathcal T with nonempty resolvent set such that either W(T)=\mathbb C, \mathcal T is maximal accretive but not sectorial, or \mathcal T is even maximal sectorial. Moreover, in all but one subcase \mathcal T can be chosen with compact resolvent.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics 
UniBE Contributor: 
Tretter, Christiane 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
00018708 
Publisher: 
Elsevier 
Funders: 
[4] Swiss National Science Foundation 
Language: 
English 
Submitter: 
Sebastiano Don 
Date Deposited: 
28 Jan 2021 18:38 
Last Modified: 
31 Jan 2021 02:59 
Publisher DOI: 
10.1016/j.aim.2020.107383 
ArXiv ID: 
1911.05042 
Uncontrolled Keywords: 
Accretive operator, Sectorial operator, Numerical range, Domain intersection 
BORIS DOI: 
10.48350/151234 
URI: 
https://boris.unibe.ch/id/eprint/151234 