%0 Journal Article
%T Counterexamples to the discrete and continuous weighted Weiss conjectures
%A Andrew Wynn
%J Mathematics
%D 2009
%I arXiv
%X Counterexamples are presented to weighted forms of the Weiss conjecture in discrete and continuous time. In particular, for certain ranges of $\alpha$, operators are constructed that satisfy a given resolvent estimate, but fail to be $\alpha$-admissible. For $\alpha \in (-1,0)$ the operators constructed are normal, while for $\alpha \in (0,1)$ the operator is the unilateral shift on the Hardy space $H^2(\mathbb{D})$.
%U http://arxiv.org/abs/0904.3831v1