view of Definition \[def2.1\] for each operator pair (linear relation) $\t=\{(C_0,C_1);\cK\}(\in\C (\cH))$ the following equivalences hold: $$\begin{gathered}
\t\in Dis (\cH) \iff (\im (C_1C_0^*)\geq 0 \;\;\text{and}\;\; 0\in\rho
(C_0-iC_1) )\label{2.2.1}\\
\t\in Ac (\cH) \iff (\im (C_1C_0^*)\leq 0 \;\;\text{and}\;\; 0\in\rho
(C_0+iC_1) )\label{2.2.2}\\
\t\in Sym (\cH) \iff (\im (C_1C_0^*)= 0 \;\;\text{and}\;\; 0\in\rho
(C_0-iC_1)\cup\rho (C_0+iC_1) )\label{2.2.3}\\
\t\in Self (\cH) \iff (\im (C_1C_0^*)= 0 \;\;\text{and}\;\; 0\in\rho
(C_0-iC_1)\cap\rho (C_0+iC_1) )\label{2.2.4}\end{gathered}$$ Moreover, the classes $Dis (\cH), \;Ac (\cH),\; Sym (\cH)$ and $ Self (\cH)$ coincide with the known classes of all maximal dissipative, maximal accumulative, maximal symmetric and self-adjoint linear relations in $\cH$ respectively.

The following proposition is immediate from Definition \[def2.1\].

\[pr2.2\] 1) In the case $\dim \cH_0<\infty$ the class $Self (\cH_0,\cH_1)$ is not empty if and only if $\cH_0=\cH_1=:\cH$.

2\) Let $\dim\cH<\infty $ and let $\t=\{(C_0,C_1);\cK\}(\in \C (\cH))$ be an admissible operator pair such that $\dim\cK=\dim\cH$. Then the following equivalences hold $$\begin{gathered}
\t\in Dis (\cH) \Leftrightarrow (\im (C_1C_0^*)\geq 0, \quad \t\in Ac (\cH)
\Leftrightarrow (\im (C_1C_0^*)\leq 0, \quad \t\in Self (\cH) \Leftrightarrow
(\im (C_1C_0^*)= 0.\end{gathered}$$

Boundary triplets and Weyl functions
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Let $A\in\C (\gH)$ be a closed symmetric linear relation in the Hilbert space $\gH$ and let $n_\pm (A):=\dim \gN_\l(A), \; \l\in\bC_\pm$ be deficiency indices of 