Everything is possible for the domain intersection ${\rm dom}\,T\cap{\rm dom}\,T*$

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

[img] Text
1-s2.0-S0001870820304114-main.pdf - Published Version
Restricted to registered users only
Available under License Publisher holds Copyright.

Download (759kB) | Request a copy
[img] Text
1911.05042.pdf - Submitted Version
Restricted to registered users only
Available under License Publisher holds Copyright.

Download (487kB) | Request a copy

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 non-empty 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 non-normal \mathcal T. We also show that all these possibilities may occur for operators \mathcal T with non-empty 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:

0001-8708

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

Actions (login required)

Edit item Edit item
Provide Feedback