is true for $T^*(I+iB)T$.

The statement in follows by tracing the above equivalences for an element $\{0,h'\}$.

\[rem3.2\] Let $\varphi=\varphi_1+\varphi_2\in \sK$ be decomposed as in . Then one has the following equivalence: $$(I+iB)\varphi\in\cdom T^* \quad \Leftrightarrow\quad (I+iB)\varphi=C_0^{1/2}(I+iC)C_0^{1/2}\varphi_1.$$ To see this, let $\eta =(I+iB)\varphi$. Then $\eta \in \cdom T^*$ if and only if $$\begin{pmatrix}   I+i B_{11} & iB_{12} \\
                                          iB_{12}^* & I+i B_{22}
              \end{pmatrix}
  \begin{pmatrix} \varphi_1 \\ \varphi_2 \end{pmatrix}
  =   \begin{pmatrix} \eta \\ 0 \end{pmatrix},$$ where $\cdom T^*$ is interpreted as the subspace $\cdom T^*\times \{0\}$ of $\sK$. Now apply .

A class of maximal sectorial relations and associated forms {#sect4}
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The linear relation $T^*(I+iB)T$ is maximal sectorial for any selfadjoint $B \in \mathbf{B}(\sK)$ and any closed linear relation $T$ from $\sH$ to $\sK$. Now the corresponding closed sectorial form will be determined. This gives the appropriate version of Theorem \[s-repr0o\] in terms of relations. In fact, the general result is based on a reduction via Lemma \[redux\] to Theorem \[s-repr0o\].

\[s-repr\] Let $T$ be a closed linear relation from a Hilbert space $\sH$ to a Hilbert space $\sK$ and let the selfadjoint operator $B \in \mathbf{B}(\sK)$ be decomposed as in . Let the operators $C_0$ and $C$ be defined 