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

Seppo Hassi*, Adrian Sandovici, Henk de Snoo

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
63 Downloads (Pure)


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)T or S = T (I + iB)T*;

where B is a bounded self-adjoint operator in a Hilbert space K and T : H -> K (or T : K -> H, respectively) is a linear operator or a linear relation which is not assumed to be closed. Using the speci fi c 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 S-F, the Friedrichs extension, and S-K, the Krein 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.

Original languageEnglish
Pages (from-to)538-564
Number of pages27
JournalBanach journal of mathematical analysis
Issue number3
Publication statusPublished - Jul-2019


  • sectorial relation
  • Friedrichs extension
  • Krein extension
  • extremal extension
  • form sum


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