  Let T : X --> X$ be a power bounded operator on Banach space. An operator C :
X --> Y$ is called admissible for T if it satisfies an estimate
$\sum_k\norm{CT^k(x)}^2\,\leq M^2\norm{x}^2$. Following Harper and Wynn, we
study the validity of a certain Weiss conjecture in this discrete setting. We
show that when X is reflexive and T is a Ritt operator satisfying a appropriate
square function estimate, C is admissible for T if and only if it satisfies a
uniform estimate $(1-| \omega|^2)^{1/2}\norm{C(I-\omega T)^{-1}}\,\leq K$ for
$\omega\in \Cdb$, $|\omega|<1$. We extend this result to the more general
setting of alpha-admissibility. Then we investigate a natural variant of
admissibility involving R-boundedness and provide examples to which our general
results apply.
