  We introduce Gutzwiller-correlated wave functions for the variational
investigation of general multi-band Hubbard models. We set up a diagrammatic
formalism which allows us to evaluate analytically ground-state properties in
the limit of infinite spatial dimensions. In this limit recent results obtained
within the Gutzwiller approximation are seen to become exact for these wave
functions. We further show that the Slave Boson mean-field theory for
degenerate bands becomes variationally controlled at zero temperature in
infinite dimensions. Lastly, we briefly comment on the variational approach to
the Anderson transition in strongly correlated electron systems.
