\,C_0^{\half}T_{\s} \,h , C_0^{\half}T_{\s}\, k),
 \quad h,k \in \dom \st= \dom T.$$ To compare these expressions with and , observe that $$(\,C_0^{\half}T_{\s} \,h , C_0^{\half}T_{\s}\, k)
 =((H_{r})_{\rm s})^{\half} h, ((H_{r})_{\rm s})^{\half} k)$$ and $$(C \,C_0^{\half}T_{\s} \,h , C_0^{\half}T_{\s}\, k)
 =(G ((H_{r})_{\rm s})^{\half} h, ((H_{r})_{\rm s})^{\half} k).$$ It is clear from that only the (selfadjoint) compression of $C$ to $\cran C_0^{1/2}T_{\rm s}$ contributes to the form , so that it is straightforward to set up a unitary mapping; cf. Corollary \[newnew\].

Extremal maximal sectorial extensions of sums of maximal sectorial relations
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Let $H_{1}$ and $H_{2}$ be maximal sectorial relations in a Hilbert space $\sH$. Then the sum $H_{1}+H_{2}$ is a sectorial relation in $\sH$ with $$\dom (H_{1}+H_{2})=\dom H_{1} \cap \dom H_{2},$$ so that the sum is not necessarily densely defined. In particular, $H_1+H_2$ and its closure need not be operators, since $$\label{s-sum-mulll}
 \mul (H_{1}+H_{2})=\mul H_{1} + \mul H_{2}.$$ To describe the class of extremal maximal sectorial extensions of $H_1+H_2$ some basic notations are recalled from [@HSS19], together with the description of the Friedrichs and Kreĭn extensions $$(H_1+H_2)_F \quad \mbox{and} \quad (H_1+H_2)_K$$ of $H_1+H_2$, respectively. In order to describe the whole class of extremal extensions of $H_1+H_2$ and the corresponding closed 