Banach Journal of Mathematical Analysis

Factorized sectorial relations, their maximal-sectorial extensions, and form sums

Seppo Hassi, Adrian Sandovici, and Henk de Snoo

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Abstract

In this paper we consider sectorial operators, or more generally, sectorial relations and their maximal-sectorial extensions in a Hilbert space H. Our particular interest is in sectorial relations S, which can be expressed in the factorized form S=T(I+iB)TorS=T(I+iB)T, where B is a bounded self-adjoint operator in a Hilbert space K and T:HK (or T:KH, respectively) is a linear operator or a linear relation which is not assumed to be closed. Using the specific factorized form of S, a description of all the maximal-sectorial extensions of S is given, along with a straightforward construction of the extreme extensions SF, the Friedrichs extension, and SK, the Kreĭn extension of S, which uses the above factorized form of S. As an application of this construction, we also treat the form sum of maximal-sectorial extensions of two sectorial relations.

Article information

Source
Banach J. Math. Anal., Volume 13, Number 3 (2019), 538-564.

Dates
Received: 23 October 2018
Accepted: 28 January 2019
First available in Project Euclid: 25 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1558749978

Digital Object Identifier
doi:10.1215/17358787-2019-0003

Mathematical Reviews number (MathSciNet)
MR3978936

Zentralblatt MATH identifier
07083760

Subjects
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

Keywords
sectorial relation Friedrichs extension Kreĭn extension extremal extension form sum

Citation

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


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