maximal sectorial extensions of the sum of two sectorial relations will be characterized in general. With this characterization one can determine when the form sum extension is extremal.

A preliminary result
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The first case to be considered is the linear relation $T^{*}(I+iB)T$, where $T$ a closed linear operator, which is not necessarily densely defined, and $B \in \mathbf{B}(\sK)$ is selfadjoint. In this case one can write down a natural closed sectorial form and verify that $T^{*}(I+iB)T$ is the maximal sectorial relation corresponding to the form via Theorem \[s-first\].

\[s-repr0o\] Let $T$ be a closed linear operator from a Hilbert space $\sH$ to a Hilbert space $\sK$ and let the operator $B \in \mathbf{B}(\sK)$ be selfadjoint. Then the form $\st$ in $\sH$ defined by $$\label{henil}
 \st[h,k]=((I+iB)T h ,T k),
 \quad h,k \in \dom \st=\dom T,$$ is closed and sectorial with vertex at the origin and semi-angle $\alpha \leq \arctan \|B\|$ and the maximal sectorial relation $H$ corresponding to the form $\st$ is given by $$\label{henill}
H= T^*(I+iB)T,$$ with $\mul H=\mul T^*=(\dom T)^\perp$. 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 $T$. Moreover, 