  The Extended Koopman's Theorem (EKT) provides a straightforward way to
compute charged excitations from any level of theory. In this work we make the
link with the many-body effective energy theory (MEET) that we derived to
calculate the spectral function, which is directly related to photoemission
spectra. In particular, we show that at its lowest level of approximation the
MEET removal and addition energies correspond to the so-called diagonal
approximation of the EKT. Thanks to this link, the EKT and the MEET can benefit
from mutual insight. In particular, one can readily extend the EKT to calculate
the full spectral function, and choose a more optimal basis set for the MEET by
solving the EKT secular equation. We illustrate these findings with the
examples of the Hubbard dimer and bulk silicon.
