A Class of Sectorial Relations and the Associated Closed Forms

Hassi, Seppo; de Snoo, H. S. V. (2020-09-19)
 
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Tiedosto avautuu julkiseksi: : 19.09.2022
URI
https://doi.org/10.1007/978-3-030-44819-6_15

Hassi, Seppo
de Snoo, H. S. V.
Editori(t)
Alpay, Daniel
Fritzsche, Bern
Kirstein, Bernd
Springer Nature
19.09.2020
doi:10.1007/978-3-030-44819-6_15
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https://urn.fi/URN:NBN:fi-fe202101262686

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© Springer Nature Switzerland AG 2020. This is a post-peer-review, pre-copyedit version of a book chapter published in Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-030-44819-6_15
Tiivistelmä
Let T be a closed linear relation from a Hilbert space H to a Hilbert space K and let B ∈ B(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 H = domT∗⊕mulT. This leads to an explicit expression of the corresponding closed sectorial form. These results include the case where mulT 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.
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