A class of sectorial relations and the associated closed forms

2019/12/14 by Hassi, Seppo, de Snoo, Henk
#47A07 #47B65 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47B44 #Secondary 47A06

paper · doi:10.48550/arxiv.1912.06846

Abstract

Let T be a closed linear relation from a Hilbert space \mathfrak H to a Hilbert space \mathfrak K and let B ∈ B(\mathfrak K) be selfadjoint. It will be shown that the relation T^*(I+iB)T is maximal sectorial via a matrix decomposition of B with respect to the orthogonal decomposition \mathfrak H=\rm dom T^* ⊕ \rm mul T. This leads to an explicit expression of the corresponding closed sectorial form. These results include the case where \rm mul T is invariant under B. The more general description makes it possible to give an expression for the extremal maximal sectorial extensions of the sum of sectorial relations. In particular, one can characterize when the form sum extension is extremal.

Related

• Factorized sectorial relations, their maximal sectorial extensions, and\n form sums
• On m-sectorial extensions of sectorial operators
• Factorization, majorization, and domination for linear relations
• Selfadjoint extensions of relations whose domain and range are\n orthogonal
• On the Maximal Sectorial Operators