July 2019 Factorized sectorial relations, their maximal-sectorial extensions, and form sums
Seppo Hassi, Adrian Sandovici, Henk de Snoo
Banach J. Math. Anal. 13(3): 538-564 (July 2019). DOI: 10.1215/17358787-2019-0003


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.


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Seppo Hassi. Adrian Sandovici. Henk de Snoo. "Factorized sectorial relations, their maximal-sectorial extensions, and form sums." Banach J. Math. Anal. 13 (3) 538 - 564, July 2019. https://doi.org/10.1215/17358787-2019-0003


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

zbMATH: 07083760
MathSciNet: MR3978936
Digital Object Identifier: 10.1215/17358787-2019-0003

Primary: 47B44
Secondary: 47A06 , 47A07 , 47B65

Keywords: extremal extension , form sum , Friedrichs extension , Kreĭn extension , sectorial relation

Rights: Copyright © 2019 Tusi Mathematical Research Group


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Vol.13 • No. 3 • July 2019
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