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.
"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