results and definitions from our paper [@Mog06.1].

Assume that $\cH_0$ is a Hilbert space, $\cH_1$ is a subspace in $\cH_0$, $\cH_2:=\cH_0\ominus\cH_1$ and $P_j$ is the orthoprojector in $\cH_0$ onto $\cH_j,\; j\in\{1,2\}$. For an operator pair (linear relation) $\t=\{(C_0,C_1);\cK\} (\in\CA)$ we let $$\begin{gathered}
\wt S_\t:=2 \im (C_1C_{01}^*)-C_{02}C_{02}^*, \quad \wt S_\t\in [\cK],\end{gathered}$$ where $C_{01}$ and $C_{02}$ are entries of the block representation $C_0=(C_{02}:\, C_{01}):\cH_2\oplus\cH_1\to\cK$.

\[def2.1\]$\,$ [@Mog06.1] An operator pair (linear relation) $\t=\{(C_0,C_1);\cK\}(\in\CA)$ belongs to the class:

1\) $Dis (\cH_0,\cH_1)$, if $\wt S_\t\geq 0$ and $0\in\rho (C_{01}-iC_1) $;

2\) $Ac (\cH_0,\cH_1))$, if $\wt S_\t \leq 0$ and $0\in\rho (C_0+iC_1P_1) $;

3\) $Sym (\cH_0,\cH_1))$, if $\wt S_\t = 0$ and $0\in\rho (C_{01}-iC_1) \cup
(C_0+iC_1P_1) $;

4))$Self (\cH_0,\cH_1)$, if $\t\in Dis (\cH_0,\cH_1)\cap Ac (\cH_0,\cH_1))$.

Note that the inclusion $0\in\rho (C_{01}-iC_1)\cup \rho (C_0+iC_1P_1)$ implies that $\ran (C_0:\, C_1)=\cK$. Therefore each of the above definitions 1) – 4) gives an admissible operator pair $(C_0:\, C_1)$.

If $\t\in Dis (\cH_0,\cH_1)$ ($\t\in Ac (\cH_0,\cH_1)$), then $\dim\cK=\dim\cH_1$ (resp. $\dim\cK=\dim\cH_0$). Therefore for an operator pair $\t\in Dis (\cH_0,\cH_1)\;(\t\in Ac (\cH_0,\cH_1))$ one can put $\cK=\cH_1$ (resp. $\cK=\cH_0$).

In the case $\cH_0=\cH_1:=\cH$ we let $Dis (\cH)=Dis (\cH,\cH)$ and similarly the classes $ Ac (\cH),\; Sym (\cH)$ and $ Self (\cH)$ are defined. In 