We apply the boundary triple technique to construct a coupling
(
A
,
B
)
(A,B)
of two dual pairs
(
A
+
,
B
+
)
(A_+,B_+)
and
(
A
−
,
B
−
)
(A_-,B_-)
relative to some boundary triples. The notion of a real dual pair with respect to the time reversal operator
\cT is introduced and it is shown that the coupling of two real dual pairs corresponding to real boundary triples is also real. If the operator
\cP \cT intertwines the dual pairs
(
A
+
,
B
+
)
(A_+,B_+)
and
(
A
−
,
B
−
)
(A_-,B_-)
for some parity operator
\cP , then it is shown that there exists a coupling
(
A
,
B
)
(A,B)
of two dual pairs
(
A
+
,
B
+
)
(A_+,B_+)
and
(
A
−
,
B
−
)
(A_-,B_-)
such that the operator
A
A
is
\cP \cT -symmetric and
\cP -symmetric in the Krein space
(\sH ,<\cdot ,\cdot <) with the fundamental symmetry
\cP . As the main result we describe proper extensions of
A
A
which are
\cP \cT -symmetric and
\cP -selfadjoint.
We apply this result to interpret the
\cP \cT -symmetric Hamiltonian considered in Bender & Boettcher (1998) as a member of a family of
\cP \cT -symmetric and
\cP -selfadjoint extensions of the corresponding minimal operator.
Keywords: dual pair; boundary triple; coupling;
\cP \cT -symmetric operator; non-Hermitian Hamiltonian