  In this note we show that for analytic semigroups the so-called Weiss
condition of uniform boundedness of the operators $Re(\lambda)^\einhalb
C(\lambda+A)^{-1}, \qquad Re(\lambda)>0$ on the complex right half plane and
weak Lebesgue $L^{2,\infty}$--admissibility are equivalent. Moreover, we show
that the weak Lebesgue norm is best possible in the sense that it is the
endpoint for the 'Weiss conjecture' within the scale of Lorentz spaces
$L^{p,q}$.
