2019/03/07 by Seppo Hassi, Hassi, Seppo, Adrian Sandovici +3
Computer Science · Mathematics · #47A06 #47A07 #47B44 (Primary) #47B65 (Secondary) #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1903.02816
openalex publication_date 2019/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper sectorial operators, or more generally, sectorial relations and\ntheir maximal sectorial extensions in a Hilbert space mathfrak H are\nconsidered. The particular interest is in sectorial relations S, which can be\nexpressed in the factorized form n S=T^*(I+iB)T
quad
textor
quad S=T(I+iB)T^*, where B is a bounded\nselfadjoint operator in a Hilbert space mathfrak K and T: mathfrak\nH\→ mathfrak K or T: mathfrak K\→ mathfrak H, respectively, is a\nlinear operator or a linear relation which is not assumed to be closed. Using\nthe specific factorized form of S, a description of all the maximal sectorial\nextensions of S is given with a straightforward construction of the extreme\nextensions SF, the Friedrichs extension, and SK, the Kre u in extension\nof S, which uses the above factorized form of S. As an application of this\nconstruction the form sum of maximal sectorial extensions of two sectorial\nrelations is treated.\n