  We introduce a method that allows for the calculation of quasi-particle
spectra in the GW approximation, yet avoiding any explicit reference to empty
one-electron states. This is achieved by expressing the irreducible
polarizability operator and the self-energy operator through a set of linear
response equations, which are solved using a Lanczos-chain algorithm. We first
validate our approach by calculating the vertical ionization energies of the
benzene molecule and then show its potential by addressing the spectrum of a
large molecule such as free-base tetraphenylporphyrin.
