  The operator-theoretic renormalization group (RG) methods are powerful
analytic tools to explore spectral properties of field-theoretical models such
as quantum electrodynamics (QED) with non-relativistic matter. In this paper
these methods are extended and simplified. In a companion paper, our variant of
operator-theoretic RG methods is applied to establishing the limiting
absorption principle in non-relativistic QED near the ground state energy
