  We prove some results about the super Poincar\'e inequality (SPI) and its
relation to the spectrum of an operator: we show that it can be alternatively
written with Orlicz norms instead of L1 norms, and we use this to give an
alternative proof that a bound on the bottom of the essential spectrum implies
a SPI. Finally, we apply these ideas to give a spectral proof of the log
Sobolev inequality for the Gaussian measure.
