Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 13, Number 3 (2019), 538-564.
Factorized sectorial relations, their maximal-sectorial extensions, and form sums
In this paper we consider sectorial operators, or more generally, sectorial relations and their maximal-sectorial extensions in a Hilbert space . Our particular interest is in sectorial relations , which can be expressed in the factorized form where is a bounded self-adjoint operator in a Hilbert space and (or , respectively) is a linear operator or a linear relation which is not assumed to be closed. Using the specific factorized form of , a description of all the maximal-sectorial extensions of is given, along with a straightforward construction of the extreme extensions , the Friedrichs extension, and , the Kreĭn extension of , which uses the above factorized form of . As an application of this construction, we also treat the form sum of maximal-sectorial extensions of two sectorial relations.
Banach J. Math. Anal., Volume 13, Number 3 (2019), 538-564.
Received: 23 October 2018
Accepted: 28 January 2019
First available in Project Euclid: 25 May 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47B44: Accretive operators, dissipative operators, etc.
Secondary: 47A06: Linear relations (multivalued linear operators) 47A07: Forms (bilinear, sesquilinear, multilinear) 47B65: Positive operators and order-bounded operators
Hassi, Seppo; Sandovici, Adrian; de Snoo, Henk. Factorized sectorial relations, their maximal-sectorial extensions, and form sums. Banach J. Math. Anal. 13 (2019), no. 3, 538--564. doi:10.1215/17358787-2019-0003. https://projecteuclid.org/euclid.bjma/1558749978