  We investigate the relation between the eigenvalues and eigenfunctions of the
BFKL and JIMWLK/KLWMIJ Hamiltonians. We show that the eigenvalues of the BFKL
Hamiltonians are also {\it exact} eigenvalues of the KLWMIJ (and JIMWLK)
Hamiltonian, albeit corresponding to possibly non normalizable eigenfunctions.
The question whether a given eigenfunction of BFKL corresponds to a
normalizable eigenfunction of KLWMIJ is rather complicated, except in some
obvious cases, and requires independent investigation. As an example to
illustrate this relation we concentrate on the color octet exchange in the
framework of KLWMIJ Hamiltonian. We show that it corresponds to the reggeized
gluon exchange of BFKL, and find first correction to the BFKL wave function,
which has the meaning of the impact factor for shadowing correction to the
reggeized gluon. We also show that the bootstrap condition in the KLWMIJ
framework is satisfied automatically and does not carry any additional
information to that contained in the second quantized structure of the KLWMIJ
Hamiltonian. This is an example of how the bootstrap condition inherent in the
t-channel unitarity, arises in the s-channel picture.
