  A new kind of symmetry behaviour introduced as partialPT-symmetry is
investigated in a typical Fock space setting understood as a Reproducing Kernel
Hilbert Space (RKHS). The same kind of symmetry is understood for a
nonhermitian Bose-Hubbard type Hamiltonian involving two boson operators as
well as its eigenstates. The phenomenon of symmetry breaking has also been
considered
