Convergence of Perturbation Expansions in Fermionic Models. Part 1: Nonperturbative Bounds

An estimate on the operator norm of an abstract fermionic renormalization group map is derived. This abstract estimate is applied in another paper to construct the thermodynamic Green's functions of a two dimensional, weakly coupled fermion gas with an asymmetric Fermi curve. The estimate derived here is strong enough to control everything but the sum of all quartic contributions to the Green's functions.