A SHORT PROOF FOR THE STABILITY THEOREM FOR POSITIVE SEMIGROUPS ON L-P(MU)

We give a short proof showing that the growth bound of a positive semi group on L-p(mu) equals the spectral bound of its generator. It is bas ed on a new boundedness theorem for positive convolution operators on L-p(L-q). We also give a counterexample, showing that Gearhart's resul t does not extend from Hilbert spaces to L-p(mu)-spaces.