by and . Then the form $\st$ defined by $$\label{henilB}
\st[h,k]=((I+iC) \,C_0^{\half}T_{\s} \,h , C_0^{\half}T_{\s}\, k),
 \quad h,k \in \dom \st= \dom T,$$ is closed and sectorial with vertex at the origin and semi-angle $\gamma \leq \arctan \|C\|$. Moreover, the maximal sectorial relation $H$ corresponding to the form $\st$ is given by $$\label{HwithC}
 H = (T_{\s})^{\times}\, C_0^{1/2}(I+i C) C_0^{1/2}\,T_{\s}=T^*(I + i B)T.$$ A subset of $\dom \st = \dom T$ is a core of the form $\st$ if and only if it is a core of the operator $T_\op$. Moreover, the nonnegative selfadjoint relation $H_r$ corresponding to the real part $(\st_H)_r$ of the form $\st$ is given by $$H_r=(T_{\s})^{\times}C_0T_{\s}.$$

Since $C_{0}^{\half}T_{\s}$ is a closed linear operator from the Hilbert space $\sH$ to the Hilbert space $\cdom T^{*}$, Theorem \[s-repr0o\] (with $\sK$ replaced by $\cdom T^{*}$, $B$ by $C$, and $T$ by $C_0^{1/2}T_{\rm s}$) shows that the form $\st$ in is closed and sectorial with vertex at the origin and semi-angle $\gamma \leq \arctan \|C\|$. Moreover, the maximal sectorial relation associated with the form $\st$ is given by $$( C_0^{1/2}T_{\rm s})^{\times}(I+i C) C_0^{1/2}T_{\rm s}
 = (T_{\rm s})^{\times}C_0^{1/2}(I+i C) C_0^{1/2}T_{\rm s},$$ cf. , , and . The identities in are clear from 