forms a proper description of the closed sectorial form $\st_K$ is essential. The results in Sections \[sect3\] and \[sect4\] allow a general treatment that will relax the additional conditions in [@HSS19].

Basic notions
-------------

Let $H_{1}$ and $H_{2}$ be maximal sectorial relations and decompose them as follows $$\label{H12}
 H_{j} = A_{j}^{\half} (I+iB_{j}) A_{j}^{\half},
\quad 1 \le j \le 2,$$ where $A_{j}$ (the real part of $H_{j}$), $1 \le j \le 2,$ are nonnegative selfadjoint relations in $\sH$ and $B_{j}$, $1 \le j \le
2,$ are bounded selfadjoint operators in $\sH$ which are trivial on $\ker A_j \oplus \mul A_j$; cf. Theorem \[s-third\]. Furthermore, if $A_{1}$ and $A_{2}$ are decomposed as $$A_{j}=A_{j\s} \oplus A_{j \infty}, \quad 1 \le j \le 2,$$ where $A_{j \infty} =\{0\} \times \mul A_{j}$, $1 \le j \le 2$, and $A_{j\s}$, $1 \le j \le 2$, are densely defined nonnegative selfadjoint operators (defined as orthogonal complements in the graph sense), then the uniquely determined square roots of $A_{j}$, $1 \le j \le 2$ are given by $$A_{j}^\half=A_{j\s}^\half \oplus A_{j \infty},
   \quad 1 \le j \le 2.$$ Associated with $H_{1}$ and $H_{2}$ is the relation $\Phi$ from $\sH \times \sH$ to $\sH $, defined by $$\label{s-s-Einz}
 \Phi= \left\{\, 